The Black Cats have yet to win in their opening four Premier League games and were also knocked out of the Carling Cup by Championship side Brighton.
Bruce's side have lost both matches at the Stadium of Light after following up the derby defeat by Newcastle with a 2-1 reverse against Chelsea.
A section of fans called for Bruce to be sacked during Saturday's loss following another summer of change in the Black Cats' squad.
Prior to the game against Chelsea, Bruce also lost Asamoah Gyan to Al-Ain and was critical of the Ghanaian striker's decision to accept a loan move to the United Arab Emirates.
However, Bramble believes demands for Bruce to be dismissed are unfair and says the players are fully behind their manager.
"Any time they call for the manager's head, it's unfair," said Bramble. "The manager has made some great signings.
"He's improved things from last season but it's going to take time to gel. It's not going to happen overnight.
"The players are all behind the gaffer. We've made some fantastic signings and it is going to take us time to bed in."