The Gunners ended their Premier League campaign by beating Everton 2-1 on Sunday.
However, they were unable to win their first league title since 2004, as Manchester City defeated West Ham.
As a result, there was a somber feeling inside Emirates Stadium after the game.
The Arsenal players stayed on the field to congratulate their fans in a lap of appreciation.
Meanwhile, manager Mikel Arteta delivered a post-match message to supporters.
Ahead of the speech, television cameras captured a disappointed Rice appearing stern with his arms crossed behind Arteta.
Fans quickly identified Rice, with one posting on X: “Declan Rice is having a strop at the Emirates.”
Another added: “I regret choosing Arsenal over City.””Regrets picking Arsenal over City.”
A third supporter joked, “Won more trophies at West Ham.”