The result not only saw Palace lift the Cup, but also qualify for the Europa League next season.
Palace won through Ebere Eze's goal and also goalkeeper Dean Henderson's penalty save from Omar Marmoush.
Lacroix told Palace TV: “First of all, I just want to say thank you to Jesus, because today everyone saw the hand of God. Everyone saw the testimony we had. I think in this team, the hand of God was on all of our backs.
“It's a proper team performance, but like I say always, it's a team, but something was different. Everyone saw today is the hand of God. Today, it was Jesus who was there and he gave us this trophy."
Lacroix continued: “I want to say thank you to all the fans also, because we won this because of them.
“I just want to say thank you to Jesus again, because this is because of him. It's an incredible feeling, thank you so much.”