The defeat leaves Postecoglou winless in his first six games in charge. The Australian is now the first permanent Forest manager for 100 years to fail to win any of his first six matches.
"The fans are disappointed. They are allowed to have an opinion on it. I heard their opinion," said a downcast Postecoglou, who was also jeered as he walked down the tunnel at full-time.
"Nothing surprises me in football. It's the climate we're in. It seems that's the way things are going. It's nothing I can control."
Postecoglou also remarked: "My responsibility is to make sure we get some wins for this football club and progress it.
"I would prefer if people were optimistic in their outlook of what I'm doing. I can only change that by winning games of football.
"Irrespective, that's not going to change the way I'm taking things on. I really believe in the process of what we're doing and I don't think we're far away from being the team that can eradicate the situation we're in at the moment and get the results."