The Clarets captain has moved to Villa Park in a deal worth £8 million as he entered the final 12 months of his Turf Moor deal.
“Tom has been a terrific servant to the club, as an individual, for the team and for the fans," said Dyche.
“He was a real ambassador around the place.
“Quite simply a situation arose this summer, where he is in the final year of his contract, there was contact from Aston Villa and I believe he has been offered a very good contract for him and his family.
“And there is a business model at Burnley Football Club, which everyone has come to understand.
“It's a very good fee for a very good player, but who is 33 with 10 months left on a contract, which has to be balanced up."