Exhibit 10.1

Execution Version

CONSENT AGREEMENT

This Consent dated as of November 1, 2013 (this “Agreement”) is among Stone Energy Corporation, a Delaware corporation (the “Borrower”), Stone Energy Offshore, L.L.C., a Delaware limited liability company (the “Guarantor”), the financial institutions party to the Credit Agreement described below as Banks (the “Banks”), and Bank of America, N.A., as Agent for the Banks (the “Agent”) and as Issuing Bank (the “Issuing Bank”).

INTRODUCTION

A. The Borrower, the Banks, the Agent, and the Issuing Bank have entered into the Third Amended and Restated Credit Agreement dated as of April 26, 2011 (as amended by Amendment No. 1 and Consent dated as of February 28, 2012, Amendment No. 2 and Consent dated as of October 22, 2012, and Amendment No. 3 dated as of April 30, 2013 and as may be otherwise amended, restated, supplemented, or modified from time to time, the “Credit Agreement”).

B. The Guarantor entered into that certain Amended and Restated Guaranty dated as of April 26, 2011 (the “Stone Offshore Guaranty”).

C. The Guarantor wishes to reaffirm its guarantee of the Obligations as amended by this Agreement.

D. The Borrower has requested, and the Agent and the Banks have agreed, to increase the Debt permitted to be incurred pursuant to Section 6.2(j) of the Credit Agreement through March 31, 2014.

E. The Borrower intends to dispose of the Oil and Gas Properties described on Annex A attached hereto (the “Potential Sale”) and has requested that the Agent and the Banks consent to the Potential Sale under Section 6.4(b) of the Credit Agreement and exclude the Potential Sale from a reduction of the Borrowing Base under Section 2.2(e) of the Credit Agreement.

F. The Borrower has requested, and the Agent and the Banks have agreed to, reaffirm the Borrowing Base at its current level of $400,000,000.

THEREFORE, in fulfillment of the foregoing, the Borrower, the Guarantor, the Agent, the Issuing Bank, and the Banks hereby agree as follows:

Section 1. Definitions; References. Unless otherwise defined in this Agreement, each term used in this Agreement which is defined in the Credit Agreement has the meaning assigned to such term in the Credit Agreement.

Section 2. Waiver and Consent.

(a) The Agent and the Banks hereby (i) consent to the departure by the Credit Parties from Section 6.4(b) of the Credit Agreement to the extent necessary for the Credit Parties

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to consummate the Potential Sale, (ii) agree that the Potential Sale shall not be charged against the basket set forth in Section 6.4(b)(i)(z) of the Credit Agreement, and (iii) waive the application of Section 2.2(e) to the Potential Sale.

(b) The Agent and the Banks hereby consent to the departure by the Credit Parties from the maximum amounts set forth in Section 6.2(j) until March 31, 2014; provided that the aggregate outstanding principal amount of Permitted Notes shall not exceed $1,500,000,000 at any time.

(c) The Credit Parties hereby waive the requirement that the Agent and the Banks redetermine the Borrowing Base by November 1, 2013 under Section 2.2(b); provided that the Borrowing Base be redetermined by November 8, 2013.

Section 3. Reaffirmation of Borrowing Base. The Agent and the Banks have reaffirmed the Borrowing Base at $400,000,000. Such Borrowing Base may be redetermined or modified in accordance with the terms of the Credit Agreement.

Section 4. Reaffirmation of Liens

(a) Each of the Borrower and the Guarantor (i) is party to certain Security Documents securing and supporting the Borrower’s and Guarantor’s obligations under the Credit Documents, (ii) represents and warrants that it has no defenses to the enforcement of the Security Documents and that according to their terms the Security Documents will continue in full force and effect to secure the Borrower’s and Guarantor’s obligations under the Credit Documents, as the same may be amended, supplemented, or otherwise modified, and (iii) acknowledges, represents, and warrants that the liens and security interests created by the Security Documents are valid and subsisting and create an Acceptable Security Interest in the Collateral to secure the Borrower’s and Guarantor’s obligations under the Credit Documents, as the same may be amended, supplemented, or otherwise modified.

(b) The delivery of this Agreement does not indicate or establish a requirement that any Guaranty or Security Document requires the Borrower’s or any Guarantor’s approval of amendments to the Credit Agreement.

Section 5. Representations and Warranties. Each of the Borrower and the Guarantor represents and warrants to the Agent and the Banks that:

(a) the representations and warranties set forth in the Credit Agreement and in the other Credit Documents are true and correct in all material respects as of the date of this Agreement (except to the extent such representations and warranties relate to an earlier date, in which case such representations and warranties shall be true and correct in all material respects as of such earlier date); provided that such materiality qualifier shall not apply if such representation or warranty is already subject to a materiality qualifier in the Credit Agreement or such other Credit Document;

(b) (i) the execution, delivery, and performance of this Agreement are within the corporate or limited liability company power, as appropriate, and authority of the Borrower and Guarantor and have been duly authorized by appropriate proceedings and (ii) this Agreement

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constitutes a legal, valid, and binding obligation of the Borrower and Guarantor, enforceable against the Borrower and Guarantor in accordance with its terms, except as limited by applicable bankruptcy, insolvency, reorganization, moratorium, or similar laws affecting the rights of creditors generally and general principles of equity; and

(c) as of the effectiveness of this Agreement and after giving effect thereto, no Default or Event of Default has occurred and is continuing.

Section 6. Reaffirmation of Guaranty. The Guarantor hereby ratifies, confirms, and acknowledges that its obligations under the Stone Offshore Guaranty are in full force and effect and that the Guarantor continues to unconditionally and irrevocably guarantee the full and punctual payment, when due, whether at stated maturity or earlier by acceleration or otherwise, of all of the Obligations (subject to the terms of the Stone Offshore Guaranty), as such Obligations may have been amended by this Agreement. The Guarantor hereby acknowledges that its execution and delivery of this Agreement do not indicate or establish an approval or consent requirement by the Guarantor under the Stone Offshore Guaranty in connection with the execution and delivery of amendments, modifications or waivers to the Credit Agreement, the Notes or any of the other Credit Documents.

Section 7. Effectiveness. This Agreement shall become effective as of the date hereof, upon the occurrence of all of the following:

(a) the Required Banks, the Borrower, and the Guarantor duly and validly executing originals of this Agreement and delivery thereof to the Agent;

(b) the representations and warranties in this Agreement being true and correct in all material respects before and after giving effect to this Agreement; and

(c) the Borrower’s having paid all costs, expenses, and fees which have been invoiced and are payable pursuant to Section 9.4 of the Credit Agreement or any other written agreement.

Section 8. Effect on Credit Documents. Except as amended herein, the Credit Agreement and the Credit Documents remain in full force and effect as originally executed, and nothing herein shall act as a waiver of any of the Agent’s or Banks’ rights under the Credit Documents, as amended. This Agreement is a Credit Document for the purposes of the provisions of the other Credit Documents. Without limiting the foregoing, any breach of representations, warranties, and covenants under this Agreement may be a Default or Event of Default under other Credit Documents.

Section 9. Choice of Law. This Agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York.

Section 10. Counterparts. This Agreement may be signed in any number of counterparts, each of which shall be an original.

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THIS WRITTEN AGREEMENT AND THE CREDIT DOCUMENTS, AS DEFINED IN THE CREDIT AGREEMENT, REPRESENT THE FINAL AGREEMENT AMONG THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.

EXECUTED as of the date first set forth above.

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ANNEX A

Excluded Asset Disposition Properties

Onshore Package –

Offshore Package

[ANNEX A TO AMD NO. 4 AND CONSENT]