Spurs sit 11th in the Premier League after their ninth defeat in 18 games this season.
Postecoglou's men have fared better in other competitions as they have progressed to the League Cup semi-finals and are well on course to reach the Europa League knockout stage.
But those extra fixtures are putting a strain on a Spurs squad missing first-choice goalkeeper Guglielmo Vicario and centre-backs Cristian Romero, Micky van de Ven and Ben Davies.
Anthony Elanga's first-half goal was enough to lift Forest into third under former Spurs boss Nuno Espirito Santo.
Tottenham enjoyed over 70 percent possession but failed to make it count at the City Ground.
"We are asking a lot of this group of players, a lot of these guys are playing every three days," said Postecoglou.
"It's only logical they are not going to be at their sharpest, but they are trying.
"A disappointing goal we conceded, but aside from that the boys worked hard and we tried to generate as many opportunities as we could considering the context of the game and how Forest play. We just couldn't get over the line."
Postecoglou's defensive options for Sunday's clash against Wolves were further depleted when Djed Spence was sent off in stoppage time.
And the club's only fit natural centre-back Radu Dragusin limped off late on.
"He (Dragusin) was a bit sore," added Postecoglou. "He hurt his ankle and said he couldn't continue so we'll have to wait and see."
