The North-West outfit secured the Spaniard's signature last weekend from Chelsea for a club-record fee of £37.1m.
Despite the 25-year-old's arrival, Parker believes that United need to add another midfielder and strengthen defensively before they can feel confident of reaching top four.
"I would love to see David Moyes go out and buy at least one more player before the window closes," Parker told talkSPORT.
"I don't know whether Juan Mata's arrival will be enough to guarantee a Champions League spot, especially when you look at Man United's present form and performance level."
United currently sit seventh in the Premier League table, 14 points adrift of leaders Arsenal and six points below fourth-placed Liverpool.