Dean Huijsen proved the matchwinner as the Cherries won 1-0 on Thursday night.
Postecolglou said afterwards: "It is not good enough. We again fell into the trap of starting the game really well, we were in control and then we conceded a really poor goal.
"Then we kind of lost our way a little bit and allowed Bournemouth to play the game that they wanted to. We had our moments in the second half but we could not get a goal.
"I don't know if they had more urgency but we have this sort of propensity to shoot ourselves in the foot when we should be controlling games. They are hard to beat here and what you should not do is give them a goal that gives them the momentum they need.
"We started to play w ith a bit more conviction at the beginning of the second half and made some good chances. Again we made things difficult for ourselves by allowing the opposition to take the game in the direction that they want.
"The fans have every right to be disappointed with the way it went tonight. I got some pretty direct feedback (on the pitch at the end) with the way that we are going at the moment and that is rightly so.
"They are all big games coming up. We have to get ourselves out of the space we are in at the minute where we can't get a real grip on the season."