The Spaniard sealed a £37.1m move to Old Trafford on Saturday evening having fallen out of favour towards the end of his two-and-a-half-year stay at Stamford Bridge.
The 25-year-old had started just 11 Premier League fixtures for the West Londoners this term, but Mata insists he holds no resentment toward the Portuguese manager, whom he thanked for strengthening him on and off the field.
In an open letter written on his personal website, Mata wrote: "Thanks to every manager I have had the pleasure to work with during my time here.
"They have all been a big help for my progression as a player. I have always respected their decisions, whatever they were; they made me more mature and a stronger person.
"[Thank you] to Jose, for making me a stronger player, because in difficult moments, I have learnt to remain positive and to keep working hard."
Mata could make his United debut in the visit of Cardiff City on Tuesday night.