Robin van Persie and Danny Welbeck both netted a brace to get Moyes' reign off to the perfect start.
However, it was noticeable Rooney did not join in the touchline celebrations for Van Persie's second, whilst he was nursing an injury as Welbeck took the acclaim for his delicate injury-time effort.
But Moyes claimed there were no problems regarding Rooney's dedication, saying: "When you cross that white line it is very difficult not to be committed.
"Lots of people are judging you.
"When you cross that white line it is up to you. I thought he was incredibly committed for the team and helped set up two goals."
After missing all United's pre-season games amid talk he wants out of Old Trafford, Rooney got an hour under his belt for England on Wednesday.
He added an additional 30 minutes to that after replacing Ryan Giggs and Moyes was satisfied with the 27-year-old's contribution.
"Wayne did well when he came on," said Moyes.
"He made a great run which opened up the chance for Robin to move the ball onto his left foot for his goal and the ball he slipped through for Danny was well weighted.