Chelsea won the Premier League title last year and finished 24 points clear of sixth-placed United. The Blues, however, are now "in a worse position than last year", according to Wright.
Tiemoue Bakayoko, Alvaro Morata, Antonio Rudiger and Willy Caballero have all arrived at Stamford Bridge this summer, but a number of key players have also left the club, including Matic.
Speaking to 'BBC Radio 5 live', the former England striker said, "they have signed Bakayoko from Monaco to replace Matic, but he has to come in and hit the ground running because Chelsea want to go far in the Champions League and defend the Premier League trophy."
"They are getting rid of players who are experienced and from who you know exactly what you're going to get."
Wright also believes the Premier League champions may struggle to score goals without wantaway striker Diego Costa. The Spaniard was a key part of last years title success, scoring 20 goals in 35 Premier League games.
"With Costa not involved you have taken away 20 goals and someone has to replicate that. "I'm not saying Morata won't do that, but when you look at Chelsea as a whole, they have a good team but are lacking depth."