"It's been great so far," said Mulgrew. "Well organised and positive."
While changing club kit might be common at Celtic, changing manager is not.
Mulgrew was Neil Lennon's first signing on taking over in 2010 and the midfielder was shocked by his exit.
Mulgrew added: "I've not seen the old gaffer. It came as a shock to me - I didn't see it coming.
"But I'm sure he made the right decision for himself and I wish him all the best. I'll always be thankful for him bringing me here.
"He was a great manager who did well for the club."