The Red Devils succumbed to a 3-0 loss at the hands of local rivals Manchester City on Tuesday night.
While questions have been raised over Moyes's position at Old Trafford, Wilkins believes that the Scotsman is still the right man to guide the club following Sir Alex Ferguson's retirement last summer.
"David Moyes had done a magnificent job at Everton, and he was the perfect choice to go in at Old Trafford," Wilkins told talkSPORT.
"It is just very unfortunate that they weren't active enough in the first transfer window they had. Had they been, we wouldn't be seeing them in the same sort of problems now.
"David Moyes is still the right man for the job though. They just didn't bring in enough players of the quality that Manchester United need."
United are seventh in the league table, 12 points adrift of a Champions League place.