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.
McLeish 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.
"I thought we showed a lot of character against Peterborough to come back from what was a horrible result in the FA Cup last weekend (3-2 defeat by Oldham). And we showed more of that character during the game to come back and get the
winner after Peterborough had equalised.
"We were a wee bit nervous for a time after they scored but credit to the players for sticking at it."