Spurs managed to handle a United fight-back to eventually win 4-3 on Thursday night.
Postecoglou later said: "We played so well, well in control of the game. It’s the way our season has gone a little bit, we self-inflicted some pain on ourselves and then we had to scramble to get a foothold again. Ended up getting a fourth and winning the game.
"It should have been a lot more comfortable than it ended up being but having said that I still can’t get away from the fact this group of players is doing an unbelievable job at the moment to ge us through this. The fact we again scored four goals and played some understanding football.
"We got tired in the second half because we have a small number of players we keep putting out there. Obviously made it tighter than the game should have been. So proud of the players efforts."
The manager also said: "We're in a semi-final of a cup competition, so I think that's something to reflect this progress for us and we've got an opportunity now, home and away to get to a final and we've earned that opportunity.
"It's one to look forward to, but we've got important games starting this week, starting Sunday, that we've still got to get through and the mentality the boys are showing at the moment, we're going to tackle these games in the same way we've tackled the ones in recent times."