Roberto Mancini's team are five points clear at the top of the Premier League after picking up 12 wins from their 14 matches.
But they have found their first Champions League campaign far harder and are now strong favourites to drop into the Europa League.
City need to beat Bayern Munich, who have already qualified, at the Etihad Stadium on Wednesday and hope that Villarreal, who have no points from their five games, can at least draw with Napoli.
Mancini has admitted that his team selections, particularly in the defeats at Bayern and Napoli, have occasionally been too offensive.
But it is that policy that has allowed them such an impressive start domestically, where they have scored a record-breaking 48 goals in their opening 14 league matches, as well as reaching the semi-finals of the Carling Cup.
In the league, they have failed to score at least three goals on only three occasions this season.
It is that kind of form that, just over three years after Sheikh Mansour's takeover, has made City overwhelming favourites to win the Premier League.
Yet it is the defensive statistics that have been troubling Mancini after seeing his team concede five goals in their three games against Bayern and Napoli.
But captain Kompany maintains there is far more to come from Mancini's side.
He said: "With us still learning to know each other better - and we are still a little bit behind on certain things - and learning a different style to what we played last year, there is still a lot to come from our team.
"The most important thing to stress is that we just stay calm.
"There is no reason to get carried away - it's a long season.
"This team is not just a load of great players. We are in this position because we have great spirit and a willingness to not be beaten, and that is important."
Mancini has attempted to calm expectations by maintaining that City will only manage one or two more rounds if they make it out of their group due to their collective inexperience in the Champions League.
But Spanish forward David Silva insists City can still go all the way and win it if they can scrape through to the knock-out phase.
The former Valencia man said: "We need to improve upon what we've achieved already and keep progressing as a team.
"Of course, we've got to do well in the Champions League and, well, we should aim to win it. Why not? I don't think that is out of the question."
At least Mancini has no injury concerns against a Bayern team that got its Bundesliga campaign back on track with a 4-1 win over Werder Bremen at the weekend, following two straight defeats.
Bayern are already through to the knock-out phase and captain Philipp Lahm admits his team are desperate to still be top of the Bundeslga for the winter break.
The Germany international has acknowledged that Bayern had been affected by their recent slump.
Lahm said: "For preference, we'd always be right at the top.
"When you've lost twice in a row, it chips away at your confidence, and you could see that at times against Werder Bremen."
Bayern coach Jupp Heynckes may choose to rest players for the trip to the Etihad Stadium, with a game at Stuttgart to come on Sunday.