City's previously strong grip on top spot in the Barclays Premier League was loosened as they were held at West Brom and beaten at Sunderland over the holiday period.
But Roberto Mancini's men put those frustrations behind them on their return to the Etihad Stadium, where they are unbeaten since December 2010, as they comfortably saw off Liverpool 3-0 on Tuesday night.
Milner, scorer of the third goal, told City TV: "It was an important game for us.
"We had a couple of disappointing results over the Christmas period. We know it is a critical time over any season and (we needed) to get the momentum back.
"We set our standards very high and the first half was not good enough the other day. We probably still did enough in the second half to win it but it is a learning curve.
"We need to make sure we learn from those sort of experiences and I think it shows how much character and ability there is in the dressing room that we can come back 48 hours later."
City had been expected to win comfortably at The Hawthorns but were frustrated as a well-organised West Brom side defended deeply and claimed a goalless draw.
The Sunderland game was heading for a similar outcome until the Black Cats broke away in injury-time to snatch a winner through Ji Dong-won.
Milner, who turns 26 on Wednesday, said: "The manager was obviously very disappointed with us but no more so than we were as individuals and as a team.
"We didn't quite have the luck over the last two games but last night [Tuesday] it was good to get off to a good start.
"We kept the pressure on, defended very well and got a very good victory."
City took charge against Liverpool after Sergio Aguero's speculative 10th-minute shot from distance was misjudged by Jose Reina and bounced in for the opening goal.
Yaya Toure doubled the advantage with a firm header from a 33rd-minute corner and Milner, after a spell of Liverpool pressure, made victory certain from the penalty spot 15 minutes from time.
City had to play out the closing 17 minutes with 10 men after Gareth Barry was sent off for two bookable offences but they did so with little alarm and even hit the post through Adam Johnson.
Milner said: "Liverpool are a very good side, you can see that from the side they put out and the players they brought on off the bench.
"They have got quality all over the field and it was always going to be tough.
"To win the game like we did, and pretty convincingly as well, down to 10 men, was good.
"That showed the quality and determination and what we are about as a team."
Milner has impressed this season despite not being a regular starter and could be set for an enhanced role in the coming weeks as key man Yaya Toure departs for the African Nations Cup.
Toure and his brother Kolo are expected to join up with the Ivory Coast for the tournament in Gabon and Equatorial Guinea after this weekend's FA Cup third-round clash with Manchester United.
Milner, however, is not thinking about his individual prospects despite the lift of getting on the scoresheet on Tuesday night.
He said: "It was nice to get on it and put it away.
"It was important to get the victory, that was the main thing.
"All the boys have done brilliantly. We need to make sure we take this momentum because the games keep coming thick and fast."