He was bumped up the pecking order following an injury to Brazilian first-choice keeper Alisson.
Adrian saved Tammy Abraham’s penalty as Liverpool won 5-4 in the shootout.
“He’s loud in the dressing room already,” said Klopp. “I don’t think he’s won a lot in his life so it’s good for him to win it. He made some unbelievable saves, both keepers did, so I’m really happy for him.”
The game finished 2-2 in 120 minutes after Abraham won a controversial penalty in the 101st minute – Adrian appearing to get the slightest touch to the striker’s knee.
But the Liverpool keeper made up for any involvement in the decision – which was checked by VAR before Jorginho slotted it past Adrian – by becoming the shootout hero.
Centre-back Virgil Van Dijk said he told Adrian he would steal the limelight.
“I said before the game that anything can happen in a final and in the end the penalties decided the game,” Van Dijk told BT Sport.
“I told Adrian before the penalties he could be the hero – he did it so I’m happy for him and for the club.”