It was a first victory of the Premier League campaign for Palace, with Jean-Philippe Mateta's 31st-minute goal proving decisive at Selhurst Park on Sunday and leaving Spurs' Australian boss clearly frustrated.
Postecoglou had handed the hugely promising 17-year-old Mikey Moore a first Premier League start, but admitted he was not pleased by how his side as a whole seemed to lose their way and let the home team dictate the encounter.
"It was a game that turned into a bit of a battle, a lot of stop-starting and standing around, and we didn't deal with that really well at all. We didn't get to grips with the nature of what was transpiring out there," said the Australian.
"They dealt with it better than we did. It was just a game where we needed to stay composed, not falling through the trap of trying to play the game that ultimately Palace wanted to play.
"It was battle after battle, duels, stop-starts and we needed to be a lot more clear-headed about how we deal with that.
"I just think we directed our frustration the wrong way."
Postecoglou was pragmatic when asked about Moore's performance, replying: "It wasn't really a great game for anybody out there, from our perspective.
"But Mikey, every time he is out there, I think he will be a better player, and the more we can get him out there in that sort of environment, then he'll keep thriving.
"I'm sure he would have learned a lot today, but the kind of team we want to be, the way we want to play, we need to be a lot more composed in the way we deal with certain things to not let the game get out of control."
Captain Son Heung-min sat out the midweek Europa League victory over Dutch side AZ Alkmaar and was again not involved on Sunday, with Spurs clearly missing the South Korean star.
Three points at home meant the Eagles avoided slipping to their worst-ever Premier League start, the first time since 1992-93 they had not tasted victory at least once after eight top-flight matches.
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