City fell a massive eight points behind United on Sunday following their 1-0 defeat at Arsenal, effectively ending their title hopes with only six games remaining this season.
However Lescott insisted City would not give up until it was mathematically impossible to catch leaders United.
"It's out of our hands but we've got to keep going and if United slip up then we've got to be there to capitalise," Lescott said. "If they don't, then obviously it's going to be impossible for us to catch them now.
"We're professional and we owe it to the fans that we're not going to roll over and die. We've got to apply ourselves in the right way in every game," he told the Manchester Evening News.
Lescott also said City's players were determined to avoid the nightmare scenario of United clinching the title at Eastlands in the Manchester derby on April 30.
"We don't want to let them win it at (Eastlands)," Lescott said. "We'll do everything in our power not to let that happen."
Source: AFP
Source: AFP