Arsenal were on course to win a historic double when Kai Havertz gave them the lead against PSG after just six minutes.
Ousmane Dembele then restored parity from the spot just after the hour mark, and as the clock ticked over, the game ended in penalties.
Eze was the first Arsenal player to miss, but he was rescued by David Raya following his save from Nuno Mendes.
Gabriel then stepped up to take their fifth and ultimately final penalty, sending his effort well over the crossbar.
Speaking to TNT Sports after the game, Rice admitted they were ‘devastated’ about their misses, but backed them to comeback.
"(They are) devastated to miss a penalty in a Champions League final, obviously It's not nice. But we love them and we're with them,” he said.
“It happens in football. They're not going to be the last players to miss penalties in finals.
"Everyone's missed a penalty and without those two this season we wouldn't have won the Premier League, that's for sure.
“Gabriel, I've ran out of words for him as a person as a player. Ezo has had some crucial goals for us this season. It happens, It's football and it's cruel. We take positives and we keep going."