Two things I think about this:
Firstly, I think it was always going to be impossible NOT to be labelled arrogant when the money came. I was arguing with a Spurs fan the other day, who was making the usual claim of 'City fans were alright before the takeover, now they're all arrogant w*nkers'. But this attitude (on the part of opposition fans and the media) would have prevailed however we conducted ourselves. Better performances breed higher expectations, and given the huge and sudden rise in performance levels, the increase in expectations was always going to look like arrogance. It's also linked to the pitiful and myopic 'established elite' mentality that many seem to have, exemplified wonderfully by Green's 'City in the Champions League, don't make me laugh' comment. In other words, we're labelled arrogant because obviously only Liverpool and Man Utds' fans are entitled to think they'll win most games.
Secondly, I do think it's important to see the value in other teams. I find that simply commenting on the strengths of another fan's team when you're having a chat will quickly dispel any suspicion of arrogance they may have. And it's good practice, too: do this often enough, and you find yourself being a bit more objective in your appraisal of the opposition. Confucianism innit