Greg Halford headed the home side in front, but Scott Wootton levelled things up before Elliott Ward - one of two loan signings this week - powered home from a corner in the last 10 minutes to hand Forest victory.
The result guides Forest to ninth in the npower Championship and within three points of the play-offs but McLeish was quick to argue a case for more newcomers.
He said: "It's no secret that we are still looking to bolster the squad and if we are going to have a real go at the play-offs we need three or four players to come through the door.
"We know what the January window is like - it's very difficult - and, no doubt, we will hit a brick wall with some of our efforts. But we are doing our best to improve the squad - and I don't just mean in numbers.
"It's important that we bring players with the right DNA to play for Forest - and they must enhance the group not just add to the roster."
Peterborough boss Darren Ferguson was left to rue the fact both Forest goals came from dead-ball situations.
He said: "To lose two goals and the game to two set-pieces is very disappointing because I thought a draw would have been a fair result.
"I am repeating myself a lot this season but I told the players afterwards that it was another game we should not have lost but it was frustrating to concede the way we did. Forest don't have too much height in the team for a Championship side but their two tallest players have got the goals from headers.
"Things went against us at times. I have seen the first goal and I'm still not convinced that it was over the line but the referee's assistant decided from 40 yards away that it was. We should have also had what I thought was a blatant penalty but there's no point in talking to officials about things like that."
- Sports & Recreation
- Scott Wootton