The Brazilian goalkeeper produced his 11th clean sheet of the Premier League campaign – joint-third-most among his peers – with a string of impressive saves at Stamford Bridge to keep the hosts out.
And Fabinho told Liverpoolfc.com: "It's always important to keep a clean sheet, to defend good. I think we have to thank Alisson again.
"This season it happened regularly that we need Ali to help us. He's been our best player this season and he showed again why. We have to defend better.
"The work of the team was really good. Some of the players, like Kostas and Curt and the other players, started the game and did well. It was not easy for them because I don't remember the last time Curtis started a game.
"But we have to keep working and try to get better and better for the next game."
Fabinho believes the Reds' performance was much better against Chelsea, following the preceding defeat by Manchester City, but accepts further improvement is required, with Arsenal next up at Anfield this weekend.
The midfielder said: "We need to create more, get more people in the box, create more chances to score.
"I think it was a good game from us. Chelsea is a good team. Of course, both teams are not in a good moment but, in the end, we take the one point."