Roberto Mancini's side dropped points for the second week running after a draw against Stoke City last weekend was followed with a 3-3 tie against Sunderland on Saturday.
City's draw against Martin O'Neill's men means Manchester United could pull five points clear with victory over Blackburn Rovers on Monday.
But, despite the potential five-point gap, Kompany maintained City will continue to fight and not focus on the results of their rivals.
“I don't really look at United's games with much interest," he told City TV. “The reality is it is not in our hands anymore. For us to get back in the race for the title we need other teams to take points away from United and we [need to] finish the job when we play them at Eastlands.”
Kompany rejected claims that the pressure of keeping pace with United has taken its toll on the City squad.
“It wasn't nerves, we didn't do enough," Kompany continued. “It was not a good performance and we didn't do enough to win the game. It is not nerves - there is nobody in the team who has not been in this situation before in another league.”