The 28-year-old came on as a substitute at half-time for Marouane Fellaini but was unable to stop the tide, with his side conceding two more goals in the second half.
Mata told BBC his Man United team-mates to pick themselves up and move on.
He said: “This is a painful result. From the first minute it started very badly.
“It is just three points, we have another important game in a few days so we need to learn from our mistakes”
Juan Mata calls on his Man United team-mates to move on quickly from their Chelsea defeat
“I felt that when we were close to their goal they scored, every time, and that was the key to the game.
“It is just three points, we have another important game in a few days so we need to learn from our mistakes.”
United now sit in seventh in the table, six points behind leaders Manchester City.
Chelsea have moved into the Champions League places, only a point off the table toppers.
Jose Mourinho will want to put his Stamford Bridge homecoming humiliation behind him when they host Burnley next Saturday.
Antonio Conte takes his Chelsea side to Southampton on Sunday.