Blues were guilty of poor marking when Aston Villa striker Gabriel Agbonlahor grabbed the late winner in the recent derby clash at St Andrew's.
City then paid the penalty for being exposed at two set pieces as Bolton earned a 2-1 win last weekend.
McLeish knows it is crucial to avoid such mistakes ahead of Saturday's clash with Burnley at Turf Moor.
The former Scotland boss said: "I have spoken to them and they have simply got to learn from the naive moments that we've had since the beginning of the season.
"We have made a solid start with seven points from seven games. If we continue that progress, we will be there or thereabouts in terms of retaining our Premier League status.
"I don't think there is any doubt about that. We've not looked out of place against any team so far in the Premier League.
"But it is a learning process for some of them. They certainly believe in themselves but they will find the little minor details is the difference between the Championship and the Premier League.
"You have to learn some hard lessons. I did it myself when I was a young player. I studied my mistakes and said I'll do things differently next time.
"That's what the Roger Johnsons and Scott Danns in the current side have got to do."
McLeish has the option to make changes now the likes of Franck Queudrue and Liam Ridgewell are available after injury.
He added: "In terms of defensive options, it is a lot healthier. We have got a strong squad from which to select. It gives me a selection headache.
"But I would rather have that than having to shift players into unfamiliar positions. The next thing will be players frustrated at not playing.
"That's up to the players in possession of the jersey. If the guys in possession are doing well, the other fellows don't have a grievance."
Full-back Stuart Parnaby and midfielder James McFadden could also be fit to face Owen Coyle's side.
Striker Cameron Jerome is also on course to return after the international break in two weeks after suffering an ankle injury against Portsmouth in mid August.