An eight-minute period before half-time, where Burnley scored three goals to turn the game around, undid an excellent start from Palace who had stormed into a 2-0 lead.
And despite the Eagles dominating the second-half and creating some good chances, the visitors held on for the win.
Lacroix, making his 80th appearance for Palace, said the manner in which they conceded the goals made it a particularly frustrating evening.
“I think we lost our focus for 10 minutes,” he said. “And we conceded three goals in these 10 minutes.
“So I think it's a big mistake from us. We are a little bit frustrated about that, about this result.
“We could give done better for the fans. I think we lost our concentration and this is not professional.
“We have to work on this, because we want to have a successful season. If we reduce these types of mistakes, we can still have a beautiful season.”
Despite a disappointing night, the bright spark for Palace was two goals from Jørgen Strand Larsen on his home debut.
“I’m happy for my teammate,” Lacroix added. “I think he is already part of the group, it feels like he’s been here for a long time.
“I was happy to see him score today and I think the fans are also happy \[with Strand Larsen\].”