Bruce took over the role at St James' Park this summer following the departure of Rafa Benitez for Dalian Yifang.
"He does get a lot of criticism and it is unjust. Criticise him after Christmas if he hasn't gone well for sure, but not now," Lee, who was speaking on behalf of GentingBet, told the Chronicle.
"I think he's found himself in this situation because he has replaced Rafa Benitez. Who wouldn't take some flack after that?
"There is nobody really that Newcastle could have brought in after Benitez that would have been immune because the fans loved Rafa.
"I've always said that the best managers at Newcastle have been Kevin Keegan and Bobby Robson. They got the area, the people and the fans. They understood what it meant and I think Steve Bruce does as well.
"I don't care if he managed Sunderland. So what. He has seen the opportunity of managing the club he idolised as a boy and he took it."