Matic was reunited with former Chelsea boss Jose Mourinho at Old Trafford in the off-season, and has made a strong start to life with the Red Devils.
"The selling of Matic to Manchester United as far as I’m concerned was an absolute disgrace, because that should never have happened," Wilkins said on BBC Radio 5 Live.
"He [Matic] is going to be the difference between Manchester United winning and Manchester United not winning this year."
Wilkins was also unimpressed with Chelsea's decision to break the bank on a replacement for Matic, rather than promoting one of the club's homegrown talents.
“Chalobah went for £6m,” Wilkins said. “I can’t quite see that at £6m. I don’t really see the differential between Bakayoko at £40m and Chalobah at six.
“I can’t see £34m difference between the two guys. Chalobah just comes back from the Under-21 European Championships and all of a sudden he is bombed out for £6m.
“£34m comes in and we sell the best holding midfield player in the country (Matic) to one of our biggest rivals.
“I can’t really see how that happens.”
Despite a 1-0 win over Manchester United on Sunday Chelsea are still in fourth place in the Premier League, nine points off pace-setters Manchester City.