The 41-year-old Scotsman was appointed the Cardiff manager in June 2011 and led them to promotion to the Premier League at the end of last season.
"[He is] the best young British manager," BBC Sport quotes Bellamy as saying.
"What he's done for this club in such a short space of time is nothing short of remarkable. He's responsible for the connection between the fans and the players.
"I can only talk from a player's point of view and it isn't for me to dictate to anyone, certainly above me. But the simple fact is I'm very fortunate to be working with the guy."
Cardiff are currently 14th in the Premier League table with eight points from seven matches.