Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement (Form S-8 No. 333-231260) pertaining to the 2012 Stock Incentive Plan, as amended, the 2019 Stock Incentive Plan and the 2019 Employee Stock Purchase Plan; the Registration Statement (Form S-8 No. 333-237193) pertaining to the 2019 Stock Incentive Plan and the 2019 Employee Stock Purchase Plan; and the Registration Statement (Form S-3 No. 333-239499) pertaining to the Prospectus of Trevi Therapeutics, Inc., of our report dated March 25, 2021, with respect to the consolidated financial statements of Trevi Therapeutics, Inc. included in this Annual Report (Form 10-K) for the year ended December 31, 2020.

/s/ Ernst & Young LLP

Stamford, Connecticut

March 25, 2021