Baines, 28, said: "His contract was running down so there was a possibility but we were hoping he stayed.
"He didn't and we wish him well. I'm sure he'll do a good job at Manchester United, he's a great manager."
Baines' full-back partner at Goodison, Seamus Coleman, agreed.
He said: "David will be a brilliant success at United. He is a great football man."