Fabinho admits Liverpool were once again indebted to their player of the season Alisson Becker after they ended their worrying run of defeats.
And the midfielder admits the Reds have to become more adventurous going forward if they are to salvage any hope of Champions League qualification.
Liverpool remained in eighth place after a goalless draw at Chelsea on Tuesday evening which prevented a fourth successive loss but has left them seven points adrift of the top four, having played a game more than most of the main rivals above them.
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Alisson made important saves from Kai Havertz in each half to earn the Reds only a fourth clean sheet on the road in the Premier League this season, although three have come in the last five such games.
Jurgen Klopp changed three of the back four in response to Saturday's dismal 4-1 capitulation at Manchester City - with a further three players brought in, including midfielder Curtis Jones for his first league start since October - and Fabinho believes Liverpool merited their shutout.
"It's obviously important to keep a clean sheet and to defend good," he said. "But I think we have to thank Alisson again. This season it has happened regularly that we need Ali to help us and he has been our best player this season. He showed again why.
"We had to defend better and the work of the team was really good. Some of the players like Kostas (Tsimikas) and Curtis, it's not easy for them (coming in). I don't remember the last time Curtis started a game but he did well. But we have to keep working and try to get better and better for the next game."
Liverpool have had only five shots on target in their last two games and have now failed to score in seven away Premier League games this campaign.
And Fabinho admitted: "We need to create more, get more people in the box, create more chances to score. But it was a good game from us, Chelsea are a good team. Of course both teams aren't in a good moment but at the end we take the one point."
The Brazilian had two chances at the end of the first half to score his first goal of the campaign, the second of which was deflected wide off the head of Chelsea defender Wesley Fofana.
And, speaking to LFC TV, Fabinho added: "I was in a good position, I had a similar ball two minutes before that and I tried to control it and the second ball came and the shot was the good choice but the defender did really well."
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