At the final whistle, Rice was seen confronting Gabriel in an angry conversation.
The result leaves the Gunners 13 points behind Liverpool in the title race, despite having a game in hand.
After a poor defeat to West Ham, Mikel Arteta’s side once again failed to find the net, highlighting their striker issues.
"(We showed) unquestionable character, how much wanted it and tried. We dominated the game. We tried in many different ways. We insisted but lacked that spark, that final pass to unlock a well organised team. We have to generate more shots on target," he told BBC Sport.
"Very different standard (to the West Ham defeat). We defended with energy, purpose, fight, willingness to make things happen. It wasn't because we lacked that. We tried until the end but weren't able to do it.
"It was same a week ago, two weeks ago, three months ago. The only thing we can do is win our matches and see how many points we get. It doesn't feel good. We're here to win."