Finishing as runners-up in Group D means City will be paired with a group winner in Monday's draw.
Barcelona, Borussia Dortmund, Real Madrid, Paris St Germain and Atletico Madrid are potential opponents in the knockout stage, suggesting City will have their work cut out to progress.
The Blues are, however, working with an expensively-assembled squad and consider themselves to be a match for anyone.
They recovered from two goals down to beat reigning European champions Bayern Munich 3-2 on Tuesday and, despite manager Manuel Pellegrini getting his sums wrong in Germany, Milner insists City are full of confidence heading forward.
The England international said after netting the winner at the Allianz Arena: "It couldn't be any tougher than this. Bayern are the reigning champions and have been to three finals in the last four years.
"They are obviously one of the top teams and have been for the last few years.
"So to come here and win is pleasing and, hopefully, shows the quality we have and gives us a big confidence boost going forward.
"We'll take anyone in the next round. We'll just concentrate on us.
"It'll be a tough team but, after this, we'll take confidence and know we can progress."
Milner also believes that a midweek boost in continental competition has set City up perfectly for a crucial top-of-the-table Premier League clash with Arsenal on Saturday.
He added: "The buzz, confidence and momentum from Munich will be more important going into the weekend.
"Arsenal are top and full of confidence as well, so it's a big game."