The south-coast club led twice through Graziano Pelle and Scott Dann's own goal at St Mary's Stadium on Saturday, but eventually fell to a 3-2 defeat as former boss Alan Pardew enjoyed his return to one of his old stomping grounds.
Marouane Chamakh cancelled out Pelle's early opener, before Yaya Sanogo and Chamakh's second turned the game in Palace's favour, with all the goals arriving in the first half, leaving Koeman frustrated.
"I think the defeat came out of our poor first half defensively. Normally that's one of the strengths of the team," he said.
"We made a lot of mistakes so they got a lot of opportunities and they scored three times, and that's not usual.
"Defensively we didn't work together and we didn't have the concentration we usually have.
"It's not normal that a team like Crystal Palace - with all due respect, because they played very well - creates so many possibilities.
"At least we had a good reaction in the second half, but it wasn't enough."
Shane Long was introduced into the action shortly before the hour mark but lasted only 13 minutes, leaving the field after a collision with Joel Ward, and Koeman revealed that the forward has a suspected fractured rib.
"That's a pity because he's doing well," Koeman said.
