Rice was named man-of-the-match after the 3-1 victory on Wednesday night.
He said afterwards: "Bayern Münich have been incredible this season; their record speaks for itself. We knew the magnitude of the game tonight. On these big Champions League nights here, we just feel it. There's something in our tummies that wants to make us go out there and win. We had that again tonight.
"I think the first half was an okay performance, 1-1 was probably fair, but in the second half we were outstanding. I don't think they had a shot. That's what we've got to keep doing to teams when they come to this place, keep suffocating them. Yeah, it was a positive night."
Asked why he seems at his best on Champions League nights, Rice continued: "I actually don't know! All the boys were asking me that inside. I think I've played football for so long now at the highest level that I know what it takes to go against these big teams, stay focused and keep playing well.
"There are a lot of games going on at the minute. I actually prefer that; I'm in a state where there are games every three or four days and I'm enjoying it because I'm getting in a rhythm and probably feeling the best I've ever felt."
Quizzed if Arsenal are now favourites for the European title, Rice insisted: "That's just a lot of talk. The Champions League - you're either in or you're out. At the moment, it's only the league phase, anything can happen.
"Look at last season, Liverpool finished top last year, then they faced (Paris Saint-Germain) and they were out. We just have to take it one game at a time, stay focused and be ready for whatever is thrown at us, because on our day I think we can beat anyone."