The Netherlands international was taken off in the first half of the surprise defeat at the Nissan Stadium.
England international Danny Welbeck picked up a knock in the pre-season friendly – but the Red Devils boss revealed Van Persie was only taken off as a precaution.
“We’ve got a couple of wee worries,” Moyes told MUTV. “Robin just felt his thigh in the first half and we didn’t want to take any chances.
“Danny Welbeck felt his groin when he came on and we’ve just got to make sure they’re all OK especially with so many games coming up. We’ve still got a few games to play before the season starts when we get back home.”
Moyes added that veteran centre-half Rio Ferdinand was merely rested in favour of Jonny Evans and Chris Smalling, while Michael Carrick is currently nursing a groin strain.
“With Rio, we just decided to give him a rest,” said Moyes.
“I wanted to get Jonny Evans and Chris Smalling a game so we rested Rio. Michael just felt his groin. It’s a bit tight from last night. It’s not anything we can see keeping him out. He just missed training and the game tonight.”
The 50-year-old, who was named as Sir Alex Ferguson’s replacement in May, also revealed Wayne Rooney has started light training after the striker returned home from the club’s pre-season tour of Asia last week.
“As far as we know Wayne [Rooney] is coming on, He’s started light jogging and the feedback I’m getting from the physios is that he’s progressing. Hopefully those dates are still on track,” he added.
The home side took the lead through Marquinhos but a Jesse Lingard strike and an own goal from Masakazu Tashiro saw United enter half-time 2-1 ahead.
Yokohama equalised when Fabio planted a powerful header into the top corner and Yoshihito Fujita won it for the home side in the final minute.