Di Maria, whose side secured the La Liga title earlier this week with a win over Athletic Bilbao, claims that he would like to win the competition to make the club's supporters even happier.
"I am happy, but there's much more to come," he said.
"I hope we win more titles and I hope one of them will be the Champions League.
"I want the fans to relish this as much as we do. I'm sure we'll make them even happier in the future."
Los Blancos travel to Granada for their penultimate game of the season tomorrow night.