The former Manchester City and Blackburn boss took over from Tony Pulis in the summer.
"He is wonderful, a real manager who takes care of everything," Begovic told Dnevni Avaz.
"He was a great player, his standards are extremely high. Often in training he can still show things to the players, he is still in great shape and form."
He added: "Although the current results are not the best, I think Stoke did a great job of bringing Hughes and we are playing much better football."