Pedro Porro had Spurs ahead before Jamie Vardy found an equaliser for the hosts.
Postecoglou later said: "Disappointing night for us. First-half excellent and controlled the game but wasteful in front of goal. Second half was the same. we started off well and once Leicester scored, the crowd lifted and we lost our composure.
"It was an issue we had last year as well, we need to keep working hard and be a bit more ruthless in front of goal. At times we made poor decisions. When we are that dominant we should be out of sight.
"We do everything to score goals and we didn't score. The dominance is great but if you don't score it is meaningless. We have to be stronger in our mindset in the front third. To be that wasteful tonight is disappointing. We just weren't clinical.
"They were all (the debutants) okay. It's not our football or effort. To get results you need to be a lot more ruthless in the final third. If we don't we won't get the rewards our football should get. The responsibility is on me. That's why you coach."