Rodrigo Muniz and Ryan Sessegnon struck late for Fulham's 2-0 win at Craven Cottage.
Postecoglou said: "It's a disappointing outcome. I thought up until they scored we were really on top of them. It was a tight game and we hadn't made a save at that point and they scored a really soft goal. Then the game got away from us. It's disappointing.
"It wasn't a great game. We had a couple of chances to score."
On Tottenham's penalty shout when 1-0 down, he said: "I'll leave that to the officials, but it does seem that the fact we don't carry on hurts us at times.
"It was a difficult game. I don't think any team created too many openings. We probably had the best one at 0-0. Like I said, we conceded a soft goal that gave them the advantage.
"We made a lot of changes today which I felt might help the team. It's our challenge between now and the end of the season. European football and league games."