The Reds maintained their 100 per cent start to the new season with a 1-0 victory over Chris Hughton's side at Anfield, with Mohamed Salah scoring the goal in the first half.
Brighton, who beat Manchester United 3-2 last weekend, improved after the break and could have snatched a draw were it not for Alisson's fine save from a Pascal Gross header in the 89th minute.
Asked if Alisson was the last piece of the jigsaw for his side, Klopp told BT Sport: "Looks like it!
"He's a massive signing for us, we knew that before. It gives him confidence, of course. A few people thought around set-pieces, because he's Brazilian and comes from Italy, he's not used to it, but he leads the line and I like that and that's why we got him in."
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Klopp admitted his side's standards dropped in the second half but was happy with the way they saw out a third win from three games.
"Sometimes, the life of a manager is like this: you get three points and there's still room for improvement," he said. "In the first half, we did what we should, played patient, scored a wonderful goal and could have scored one or two more.
"The second half wasn't like that, I don't remember a big chance. The game was still open, our passing game wasn't good enough anymore. They had their chance. If they score in that situation [Gross' header] they deserve it, because they defended well. I'm very happy with the result so it's all okay.
"It's never all about the result but football is a results game. We don't have that [1-0 wins] that often, the game [usually] stays exciting, but today it was 1-0 and apart from the header chance and [Anthony] Knockaert, that was it.
"We deserved the three points and that's good. We have work to do. During the week they looked fresh but today not so much, so the manager learns as well. So far so good but we knew before the game that we had a lot of work to do."