Adrian was thrilled to help Liverpool win the UEFA Super Cup against Chelsea on his first start for the club.
Deputising for the injured Alisson, Adrian denied Tammy Abraham to seal a 5-4 penalty shoot-out success for the European champions over Chelsea in Istanbul on Wednesday.
With Alisson expected to miss several weeks due to a calf injury sustained against Norwich City in last week's Premier League opener, Adrian will have more chances to impress.
And the former West Ham goalkeeper was delighted to have made an impact on his full Reds debut as Jurgen Klopp's side made up for losing the Community Shield to Manchester City on penalties.
"Welcome to Liverpool! It has been a crazy week," Adrian said to BT Sport. "I am happy for the team, with them it is easy.
"I am happy to win the trophy. I am really happy for the fans. It was a long game but in the end it was a great finish."
Adrian was able to make amends for conceding a penalty in extra time, Jorginho converting to make it 2-2 after the goalkeeper felled Abraham.
Replays appeared to indicate contact with the striker was minimal and Adrian disagreed with the decision made by Stephanie Frappart, who became the first female official to take charge of a major men's final.
"I tried to stop when I saw him. The striker is intelligent," Adrian added.
"I touched him but he was looking for it. I told the referee I tried to stop but it doesn't matter.
"We got the title and have to enjoy tonight."
Liverpool captain Jordan Henderson accepted the Reds were not at their best against the Europa League winners but cited difficult conditions for their unimposing performance.
"It was tough. It is humid here - you can't tell on the TV," Henderson told BT Sport. "It was tough with extra time - a lot of the lads were struggling. We were trying to keep the ball and get a breather but it was a bit sloppy.
"Chelsea are a good side and this is not a great way for them to lose, like we did in the Community Shield. I'm delighted for Adrian, who is the hero tonight.
"We've got a big game on Saturday [against Southampton] so I'm delighted. We want to win as many trophies as possible. We'll take the trophy back and enjoy it, but we've got to focus on recovery for a big game on Saturday.
"We didn't play particularly well but we kept grinding in tough conditions, kept going. It's another trophy for us and it's important to keep winning. Hopefully we can continue this run of form now."