Di Matteo was No 2 to Villas-Boas at Chelsea before he took over as caretaker coach when Roman Abramovich grew impatient of his Portuguese coach.
He won the FA Cup and Champions League and Villas-Boas said: "It's difficult for Robbie. I wish him well in his career. He has achieved so much in such a small amount of time.
"His CV is now one of the best in the world. He is a European champion and an FA Cup winner. It's the club's decision. It's what they think moves them forward. I can't really comment on that."