Villas-Boas was axed on Sunday after a 1-0 defeat at West Brom was deemed the final straw for owner Roman Abramovich following a tumultuous first season for the Portuguese at Stamford Bridge.
Mata, 23, has been one of the few bright sparks for the Blues since Villas-Boas brought him to the club summer, and he expressed his thanks to his former boss.
"It hasn't been an easy day for those who, like me, are part of Chelsea," Mata said. "I would like to thank the manager and wish him luck.
"We have to keep working hard and better days will come. Thanks for your support!"
Roberto Di Matteo has been installed as caretaker manager for the rest of the season, as Chelsea look to improve on their current position of fifth in the table and qualify for the Champions League.