Blues looked devoid of energy during the opening 45 minutes after their Carling Cup triumph over Aston Villa in midweek and trailed at the interval to a goal from Sebastien Bassong.
But they dug deep and a second half goal from top scorer Craig Gardner means they have only been beaten once in front of their own fans since September 2009.
McLeish said: "The Villa game took unbelievable energy out of the players. It was an emotional night. Harry (Redknapp) might have thought we were there for the taking because of that. A lot of players were running on empty and we had to patch them up but one thing you can't deny them is our phenomenal spirit."
He added: "Spurs were fresh, having not played in midweek, and they had chances in the first half, but we could have won it in the second. We shuffled things tactically and were more effective."
McLeish brought on midweek goal hero Nikola Zigic and the Serbian international set up the equaliser.
McLeish said: "I would say that was the most effective he has been for us. He did not lose a header in the air. He is adjusting to the different style of football over here."
In injury time Tottenham defender Alan Hutton appeared to head-butt Birmingham defender David Murphy in the chest after being on the receiving end of a late challenge.
But referee Kevin Friend took no action against either player.
McLeish, who managed Hutton at Rangers, said: "Did the referee see it? He could not have seen it but I'm not here to talk about players getting sent off.
"It was a reaction from Hutton over a bad tackle on him, a split second emotional reaction."