The result brought City within three points of the Premier League leaders while they have a game in hand.
After the final whistle blew, Rice saw his captain Martin Odegaard in the centre circle and was heard shouting: "It's not over."
Arsenal manager Mikel Arteta agreed with Rice and told reporters in the aftermath: "I believe today, I believe on Wednesday a week ago because I see them every day and I know the level that we have.
"But today if they need to be more convinced, I think they are now more convinced. They were talking about it in the dressing room. It's a new league now. They were a game in hand.
"We have three points of advantage and five games to play. So everything is still to play for. So we know how much we've won it and we're not going to stop and we're going to go again, that's for sure."