England midfielder Milner struck a superb injury-time free-kick to snatch a 1-1 draw at the Etihad Stadium after a troubled afternoon against the relegation battlers.
The result left the champions seven points behind Barclays Premier League leaders Chelsea and needing inspiration to get the defence of their crown back on track.
Milner said: "We can't really afford too many more slip-ups, if any. Chelsea have a big lead now but it's down to us to see how many points we can get.
"We know, more than anyone, you have to keep going to the death and anything can happen, but I think we have got to be pretty faultless between now and the end of the season to get close."