Villa went down to their first defeat of the Premier League season last week when they were beaten 4-1 by Manchester City at the Etihad Stadium - a result that frustrated the Scot.
"I'm not going to point the finger at anybody here and now," McLeish told the Birmingham Mail.
"But I've told the players that if you don't pick up men when you're supposed to then it could cost you your place in the team.
"It happened at City but if we'd have defended like that against Dulwich Hamlet we'd have lost goals and that's a fact.
"The fact it was City then perhaps I can look at the whole thing again and say because it was them I'll throw out an amnesty.
"But if we continue to lose goals like that against other teams we're expected to take points against then it's going to be a long season.
"They were ridiculous goals - set-pieces where we weren't doing our job and picking up.
"Quite simply if that continues it will be difficult for me to keep players in the team if they aren't going to adhere to the instructions. I have told the players that."
The former Birmingham boss believes the organisation of the team was to blame, particularly from set-pieces against City, but he refused to criticise the commitment of his players
He added: "It wasn't so much getting beat in 50/50s, the problem was we didn't have enough numbers against City's numbers.
"It wasn't a case of anybody bottling out or chickening out of challenges or being out-jumped, it was a case of being outnumbered at the weekend on those two goals. It was down to organisation.
"We told players exactly what to do but for some reason there was confusion.
"We won't be allowing them to hide behind those excuses anymore. I won't accept it.
"I think if you see Richard Dunne at the weekend with Vincent Kompany's free header, he's pointing to ask players on the edge of the box to pick Kompany up.
"You actually see him pointing. Then Kompany makes the run. So whether it was too late for the three men on the edge of the box to do anything about it I don't know."