The 26-year-old bemoaned the Premier League champions's failure to convert their chances but praised the mental strength shown by his side to keep going away from home
The visitors had the lion's share of possession and chances on Sunday afternoon but were held to a 0-0 draw as Rafa Benitez earned his first point as Blues boss.
But the England international feels Roberto Mancini's men merited more and bemoaned their failure to convert the opportunities which came their way.
"We were the better side, we had the better chances and restricted them to not too many,” Milner told the club’s official television channel, City TV.
"I thought we played a good game and didn't quite get the three points.
"We have got things to work on. We need to take our chances - we had a number of corners and chances that didn't go our way.
"When we are on top in games and have territory and chances we are not quite putting teams to bed like we should be.
"Hopefully we can improve on that during the season. There are positives and negatives to take out of the game."
The former Leeds attacker went on to hail the way in which City kept Chelsea at arm's length, despite things not going their way.
He continued: "It shows mental strength because sometimes, when you have those days, it is easy to think it's not our day and sit back and let the other team into the game and have chances themselves.
"I don't think we did that. We were pretty solid and moved the ball around pretty well.
"The pitch wasn't the greatest but we tried to be positive and it just didn't happen for us at the business end."
The England international also called for his team to improve on their set-pieces in order to make the most of the dead-ball specialists in the squad.
"When you are on top of teams you are going to have set-pieces,” he added.
"We have got quality delivery with 'Kolar' [Aleksandar Kolarov] and David [Silva] and people like that.
"We need to maybe come up with a few new things and make sure we attack that ball. I'm sure the goals will come."