A 2-1 win at AEK Larnaca on Thursday saw Palace defeat the Cypriots for the same scoreline on aggregate in their round of 16 tie.
Ismaila Sarr struck both Palace goals, with the winner coming in extra-time.
“A long day, but a really important win,” Lacroix insisted, speaking to Palace TV. “I think we deserved it.
“You can see with the statistics that we shoot a lot, but they played really well, to be honest. And until the very end, we kept on going, so it's perfect.
“This is the thing that we’ve learned a lot: to be patient, to wait for the good passes, the good runs and the good moments in front of goal.
“To be honest, they did very well defensively. It was not easy, but in the end, we scored two beautiful goals.
“We could’ve scored three or four, but we didn't take the chances – we’ll take them against Fiorentina.”