Goals from Mikael Forssell and Sebastian Larsson put City in control but a Peter Crouch shot reduced the arrears before a deflected header from Yossi Benayoun rescued a point for the Merseysiders.
McLeish said: "I was very disappointed. Before the game we would have taken a draw with Liverpool. But having gone ahead 2-0, you think it is sewn up.
"The first goal they score was down to very naive players with Jermaine Pennant running at our defenders. They dived in a bit, went to ground a few times.
"But for that it could have been a fantastic result - but we still got a point and that point could keep us in the league.
"They were very fresh and you could see that in the second half. Our players were running on empty. Olivier Kapo has been struggling with flu for the past three days but I thought it was very important to include him with his quality
and his presence.
"He ran out of steam - and unfortunately he ran out of steam right at the point where the equalised but Liverpool's players were much fresher than us in the second half.
"That factor told in the sense that team hasn't played as much as we have."
McLeish added: "The players have got to pick themselves up. They are more angry than anything. They are not demoralised because they know it was a good reaction after a bad day at the office against Aston Villa last week.
"That is what I asked for - and I got that today.
"But we are paying for individual mistakes. We have got a good goal difference but lose goals through individual errors and that has cost us this season.
"There is a lot of inexperience in that team out there and they will learn from some of the mistakes they have made this season.
"There is no magic wand. I don't think we need to get paranoid about today. We have got to go along the same lines next week.
"We are due to have an away victory and we can go to Fulham and win."