"He had some discomfort in his back, and he was telling us during the first half that he wasn’t comfortable," Arteta explained post-match.
"When we assessed him at half-time, he couldn’t continue, so we had to change him."
Arteta does not yet know the severity of Rice's back problem, saying the midfielder will need to be checked ahead of four matches across three competitions before the next international break.
Arsenal face Brentford in the Carabao Cup, AFC Bournemouth in the Premier League, and Lens in the UEFA Champions League in a run that culminates with a home match against early leaders Manchester City on 8 October.
"Hopefully not [out for long], but we have to assess him," Arteta added. "It’s strange that a player like him asks to come off, because he wasn’t uncomfortable. Hopefully not, but we’ll see."
Arteta, though, is not stressing about the situation. He says it will present opportunities for Arsenal's squad players to step up, and insists these injuries are not because of the team's midweek involvement in the Champions League.
"It was already a test today because we missed five big players, but it’s what we have," he said. "We need to give trust and opportunities to the other ones – we have a game every three days and that’s the level we have to show, so let’s go for it.
"We finished the game really strong. We were very dominant; we were playing in their third and they couldn’t get out. There were moments that we played super hype, and in these derbies, the stage, the atmosphere and the energy to play there, and to play at the same pace when you don’t have the ball, and when you get it back. We lacked that composure to be much more dangerous, because we could have been."