Hull City Council said plans to renovate Hull New Theatre would not be affected by its failure to secure support from the Arts Council.
The council wants to increase the venue's capacity and improve backstage facilities in time for Hull's City of Culture year in 2017.
The Arts Council said there had been "a great deal of competition" for funding.
The council, which is contributing £6.7m, to the project, said it was "actively exploring other potential funding options".
Councillor Steven Bayes, portfolio holder for UK City of Culture and Visitor Destination, said: "Whilst the news from the Arts Council is disappointing, the Council remains committed to the refurbishment of the theatre.
"The venue is very important to the city and is absolutely critical to our plans for 2017 and beyond.
"With any project of this scale and ambition, there will be setbacks from time to time, however, we are actively exploring other potential funding options."
An Arts Council spokesman said it was keen to support Hull in its role as UK City of Culture and wanted to "keep talking" about future bids.
An £11.7m theatre refurbishment project will go ahead despite a £5m funding bid being rejected.