Well I can't talk from your perspective, all I know is that the Gooners I know, and the crowd in general from going to the matches definitely have it in for Spurs and to a lesser extent the Dippers, but there's not really been animosity towards City, more of a 'we want to be them' vibe.
It'll get more tense now for sure as we are both playing in the same pool now, but aside from expected banter I see (as an example) a lot more animosity towards City from Spurs than I do Arsenal.
I think you'd need to hire someone like (God forbid) Mourinho for that to change. Aside from the obvious jibes you'll get from every club (and which out of respect I won't reference here) City aren't really a 'dislikeable' club from an Arsenal perspective - I've always cheered them on in Europe for example and there hasn't been aggro between the teams recently either - the managers are mates, I can't think of any pre-match mind games or on-field foul play like you get against the Dippers etc. Well not yet at least!