The Trotters remain anchored in the bottom three of the Barclays Premier League after a goal from Olivier Kapo doomed them to a fifth defeat in six matches at St. Andrews on Saturday.
Bruce, who attempted to make Lee his number two a couple of years ago, said: "It would be difficult for any manager to replace Arsene Wenger at Arsenal or Sir Alex Ferguson at Manchester United given the standards they have achieved.
"Now the same is going to be true of little Sammy in replacing big Sam at Bolton. Let's be fair, big Sam did an outstanding job there for several years.
"That's the reason why big Sam was very close to getting the England job just over a year ago and that's why he has now got one of the best jobs in the country at Newcastle.
"Little Sammy needs a little bit of time to do it his way - and the one thing he's got to have now is time because five or six games in, after a new manager walks through the door, you've got to give him a chance to prove himself."
Bruce added: "If you look at any successful club - and Bolton are one - they have got continuity.
"There's going to be bad times. There have been low times for me in my six years at Birmingham but today we're sitting 12th or whatever we are in the Premier League.
"The club have stood by me and I've repaid them by being loyal, which is what you need. Then you have a chance.
"If you appoint somebody, then just throw them out, you're never going to be successful. I hope the people at Bolton give their support to little Sammy because it's a tough, tough job, believe me."