Elliot Anderson and Chris Wood had Forest 2-0 ahead at Spurs inside the opening 16 minutes. The hosts didn't reply until on 87 minutes through Richarlison.
After the 2-1 reverse, Postecoglou rued: "It's disappointing. It's a game we should never lose. One we have let slip. I'm really disappointed with the goals we conceded. The most frustrating thing outside of that is our football was outstanding. We couldn't have dominated any more than we did.
"We've seen this all year. We have just conceded poor goals and given ourselves a mountain to climb. It is not about mistakes being repeated but not having that concentration and focus for the whole game.
"We had a focus on Thursday night that we didn't seem to have at the beginning of the game and then after we conceded we knuckled down and started playing our football. You can't give teams two goal starts. There's too many games this year that we have lost in that manner and that is why we are in the position that we are."
Selection made with eye on Bodo/Glimt
Postecoglou admits his selection was influenced by their upcoming Europa League semifinal against Bodo/Glimt.
He explained: "It was pre-planned for (Micky) van de Ven and (Cristian) Romero to play 45 minutes and the same with Kulusevski and Odobert who have not played in quite a while. Everyone got through it ok I guess. That is one thing but we want to maintain momentum but we missed that opportunity.
"It is a bit of a balancing act. We have got to be ready for Thursday week, that is the big game for us. We have to have all of our players healthy and in good condition."
On facing Liverpool this weekend, Postecoglou concluded: "Another good test. Look if we play like we did today but keep our concentration levels where they should be then we can give them a game. We still need to rectify a couple of things."