The Foxes had started the game against the London club in positive fashion, creating chances.
However, Palace emerged from the second half the more dominant team and ran away with a 2-0 win.
Post-game, Van Nistelrooy told BBC Match of the Day: "I think the difference in performance from us was too big. We dropped our levels and Palace are lethal. First chance is in and it took the momentum. I think we should have had the first goal to build on.
"Palace came well out of the dressing room in the second half, they pushed us back a bit and then a goal was scored and the game changed. We dropped in intensity in the defensive bit in the pressing and that's why the momentum changed as well.
"We were speaking about Champions League opposition and the tough run we had. We wanted to show today we have improved and we did that for 45 minutes but it's about consistently performing over 90 minutes and we're not quite there yet.”