Cardiff have managed to claim just one win in the Premier League since the Norwegian took over at the club at the start of the year.
Bruce's side piled on the pressure with a 4-0 win at the Cardiff City Stadium on Saturday, but Bruce has urged the club to give Solskjaer time to prevent discouraging young managers.
"I am delighted that somebody like Ole has gone into management," Bruce told reporters. "If we are not careful, and we keep saying this week in and week out, we are going to discourage people like Ole Gunnar.
"He has had a wonderful playing career, is an enthusiast of the game and wants to stay in the game. He needs to be given time to let him manage and that goes for everybody. When you see the turnover of managers we have repeatedly in this country, it's ridiculous.
"If we are not careful, we will not have any up-and-coming young ones. It is a tough time for him but he is made of stern stuff and I wish him well."
Cardiff City currently sit in 19th place in the Premier League table.