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. 333-188808) pertaining to the First NBC Bank Holding Company Stock Incentive Plan of our report dated March 31, 2014, with respect to the consolidated financial statements of First NBC Bank Holding Company included in this Annual Report (Form 10-K) of First NBC Bank Holding Company for the year ended December 31, 2013.

/s/ Ernst & Young LLP

New Orleans, Louisiana

March 31, 2014