"Welcome to Liverpool," said Adrian as he reflected on his dramatic start to life with the Reds.
"It was a crazy week. I'm really happy for the team and really happy to get that trophy. I'm really happy to play here for Liverpool and for the fans. It was a long game, but at the end it was a great finish for us."
Chelsea struck early through Olivier Giroud, but Sadio Mane's double ensured Liverpool came back to lead 2-1 in extra time.
Adrian was then adjudged to have brought down Abraham, despite replays suggesting there was very minimal contact. Jorginho converted the penalty to leave Adrian frustrated by the decision.
He said: "I tried to stop when I saw him [Abraham]. He touched me and I touched him with my feet. I think he was looking for it. I'd have to see it again.
"I told the referee, but at the end of the day we got the trophy and we need to enjoy tonight."
Jordan Henderson, who lifted his second trophy as Liverpool captain to follow on from the Reds' Champions League triumph over Spurs back in June, was also full of praise for Adrian's role in the victory.
"It was a tough game. Chelsea are a good side. It's not a great way to lose on penalties like we did in the Community Shield, but thankfully we won this one," said Henderson.
"I'm delighted for Adrian. He has just come into the club, but he is the hero tonight. A lot has been asked of him straight from the off. It's been a great start for him and hopefully he can continue this run of form now.
"We are delighted to win. We want to win as many trophies as we can. We've got to enjoy it now, but then we must focus on recovery for a big game on Saturday (at Southampton)."