The Ibrox side scraped a narrow 1-0 win over Kilmarnock to keep them at the top of the table a result which follows defeat against Motherwell and another close call at Partick Thistle.
The victory at Rugby Park was enough to ensure they remain league leaders into the new year, despite Celtic's win over Dunfermline at Parkhead. But McLeish reckons the result had far more to do with first-class displays from his defenders rather than the front players who continue to squander chances in front of goal.
He said: "Getting the three points was our target and we did that but it was just unfortunate in the second half that we missed a few chances that could have put Kilmarnock away.
"The work-rate was fantastic and the defenders stood up to be counted whenever Kilmarnock went for goal.
"We are obviously going to have to do a bit of shooting practice and a bit of heading practice.
"The players who missed the chances are disappointed and they know that they have to be a bit more clinical. The game is never over at 1-0 but I had a good feeling today about the players at the back that they wouldn't lose a goal they handled everything thrown at us."
With goals at Rangers being in fairly short supply recently, the last thing McLeish needed was the news that one of his strikers is set to be sidelined again.
Shota Arveladze made his return against Killie after missing the last couple of games with a thigh strain, but McLeish admits including the Georgian hitman in the side again so soon was a gamble which did not pay off.
He said: "Shota is a doubt for the Dundee game now. It was a thigh strain which kept him out and everyone the physios, the coaches and Shota decided that it was a risk worth taking.
"It wasn't a serious injury and it might not clear up in time but it was a case of Shota putting the club before himself." That could mean a longer stay at Ibrox for outgoing striker Billy Dodds, but McLeish insists he is not standing in the way of his move to Dundee United.
Killie boss Jim Jefferies saw his side's impressive unbeaten run come to an end but he reckons he cannot fault his players after a gutsy display against the league leaders. He said: "If we are going to lose a game then we should lose in that way we were a bit tentative in the first half but in the second half we had a go at them."
KILMARNOCK: Marshall, Canero, Innes, Shields, Dillon, Fowler, Fulton, Mahood, Mitchell (Dargo 45), McSwegan (Boyd 66), McLaren.
RANGERS: Klos, Moore, Amoruso, Malcolm, Ross, Ferguson, de Boer, Muscat, Arveladze (Caniggia 51), Mols, Lovenkrands.