City completed a remarkable escape from the group stages after beating Roma 2-0 at the Stadio Olimpico in one of the greatest results in the club's history.
The club had looked to be heading for elimination after collecting just two points from their opening four games in Group E but a dramatic win over Bayern Munich revived their chances.
Their hopes in Rome were hampered by the absences of Sergio Aguero, Vincent Kompany and Yaya Toure but they seized their opportunity and silenced a hostile crowd with second-half goals from Samir Nasri and Pablo Zabaleta.
Milner said: "We will take it step by step but I definitely think the quality is there to go far in this competition.
"We don't want to get ahead of ourselves, but the more seasons we play in the Champions League, and the more games we play in it, the experience helps and we get better as a team."
City looked like being overrun in the early stages as Roma, and particularly Gervinho, tore into them.
But they withstood the pressure and Nasri put them on course for a famous victory with a stunning strike on the hour that flew in off the post.
Roma hit the woodwork in response through Kostas Manolas and Martin Demichelis cleared off the line from Mattia Destro but City held firm.
Zabaleta finished the job four minutes from time after being teed up by Nasri
CSKA Moscow's defeat at Bayern Munich confirmed their progress to the knockout stages.
The mood in the City dressing room was in marked contrast to a month ago after they suffered a dismal defeat to CSKA at home.
Milner said: "We started the season slowly and were a bit up and down.
"Our Champions League campaign didn't get off to the best of starts - the draw wasn't kind to us again, we didn't perform the way we can, and we put ourselves in a bit of a situation.
"We managed to get out of that situation and qualify, and that's the main thing
This club needs to be in the latter stages of the Champions League and we have managed to do it.
"This team responds when we need to win games - we did it last year in the Premier League and now we have done it again in the Champions League, by winning these two.
"We had a bit of help from the other game, but to beat Bayern Munich and Roma to qualify, and do it with a number of injuries, shows the amount of quality there is right through the squad."
Source : PA
Source: PA