Rice was substituted late into the 2-0 win on Saturday.
Arteta said: “Yeah, he was cramping.
“He hasn’t had the longest pre-season ever. But he was really trying and he put an unbelievable performance again. At the end he was struggling a bit.”
Rice and Bukayo Saka started just 37 days after England's Euros final defeat to Spain.
“I’m not surprised,” said Arteta. “That was their mentality straight away after the last game they said: ‘I’m gonna be ready for the first game’.
“I spoke to them after the summer, and tried to arrange a plan. They wanted to come back and be here early.
“They were already getting prepared when they were on holidays. This is the mentality that we need. If players are doing that compromise it will grow around the team and they will step up the level. That’s what we need.”