DUP MP Gregory Campbell has said the issue of changing the name of the city from Londonderry to Derry is "dead".
Derry City Council failed to reach agreement at a meeting on Monday. Proposals were put forward by Sinn Fein and the SDLP but both were rejected.
Mr Campbell said an equality impact assessment showed 3,000 people in favour of a change, but 9,000 were against it.
"That result is very clear - the issue is dead, and it's time to move on."
Mr Campbell criticised Sinn Fein for "engaging in wild goose chases".
"They are still campaigning for a united Ireland, they are not going to get that either.
"They have to get used to the fact you campaign for something and you don't always get it, but that's life, you live it and move on."
The SDLP had proposed to defer any action until a working group had been set up and further consultation carried out.
Sinn Fein proposed that the council should go ahead with its original plan to approach the privy council about changing the city's official name to Derry.
Sinn Fein Councillor Kevin Campbell said it is accepted that the "majority of people, when referring to the city, call it Derry".
"Even unionist organisations proudly bear the historic name Derry. What is the SDLP's problem with proceeding with a council policy which it has already endorsed," Mr Campbell added.
"This debate has been exhaustive and I believe that it is time that decisive action is taken to restore the rightful and historic name to this city.
"Further prevarication will only add to the confusion when attempting to market the city with a plethora of names."
SDLP councillor Helen Quigley said she was disappointed the party's proposals were voted down.
"The SDLP has always been fully supportive of moves to have Derry officially recognised as the name of our city.
"Unfortunately other parties including Sinn Fein would rather play political games and voted against this idea and a subsequent plan for group leaders to come together to work out a possible way forward," she said.