Illness ripped through an already injury-hit Spurs squad during what Postecoglou described as a “really tough week” in the build up to their trip to Old Trafford.
But Spurs twice came back from behind to earn a point in Manchester.
A proud Postecoglou said: “I'm delighted. I thought we played really well. It wasn't the greatest of starts being a goal down particularly here. Our response was outstanding and our football after that was really good. In the second half we really controlled the game. We've had a really rough week off the field with illness and other things.
"[Dejan Kulusevski] had not trained all week, Skippy was under the weather, so was Destiny [Udogie] and two or three others have all struggled with it this week. All year we've just got on with it. It was a big game, particularly away from home. [Cristian] Romero was outstanding as the skipper.
“I thought it was an outstanding performance considering the challenges we had in putting a team out there today.
“I could not be prouder of them. I thought we were unlucky not to win the game. Irrespective of that, the performance and the effort the boys put in was first rate.
“Timo [Werner] has had two training sessions with us, hasn't played a game in ages, I just thought Pierre-Emile Hojbjerg coming in, Rodrigo [Bentancur] and even Skippy, who haven't started games in quite a while... it took an enormous effort from the lads and credit to them.”