The South American midfielder completed a £39m move to Liverpool FC to become the first Anfield arrival of the 2018 summer transfer window.
Fabinho was previously linked with a move to Arsenal and Manchester United but the Reds acted quickly to wrap up a deal back in June.
Klopp, though, waited until the 20 October to hand Fabinho his Premier League debut after the summer signing started in a 1-0 win at Huddersfield Town last weekend.
The former Real Madrid star came off the bench for the final 21 minutes of the 1-0 win to make his first Premier League appearance.
“He has all the qualities; hard challenges, good offensively, good defensively, quick, good shooter, fantastic set-pieces, good header – all these things,” Klopp told Liverpool FC’s website.
“Strategic too, he is good strategically in the right moment. But it’s been a different system. We just play different and that always needs time. He’s just a fantastic addition and can improve us from a specific moment on.
“Go back a year and look at Andy Robertson. He played one or two games by this stage, not too many, and then he became the player he now is.
“We cannot – I cannot – shorten the time it takes [to settle]. Maybe somebody can but I can’t. Ilkay Gundogan needed more or less half a year [when Klopp was in charge at Borussia Dortmund] without being in the squad more or less. After that he played pretty much each game. That’s how things go.”
Fabinho has only started one game in all competitions this season after the defensive midfielder was named in the starting line up for their 2-1 loss to Chelsea FC in the League Cup third round.
The former AS Monaco midfielder has made cameo appearances in a 3-2 win over Paris Saint-Germain and a 1-0 loss to Italian side Napoli in the Champions League group stage.
The 25-year-old arrived at Anfield with a big reputation after Fabinho helped AS Monaco to win the Ligue 1 title ahead of PSG in the 2016-17 season.
He also played a big role in their run to the Champions League semi-finals in the same campaign before AS Monaco lost to Juventus in the semi-finals.
Liverpool FC’s 1-0 win against Huddersfield Town helped the Merseyside outfit to keep pace with Premier League leaders Manchester City.
Mo Salah scored a first-half winner to net his fourth goal in the Premier League this season to silence his critics following a slow start to the season.
Liverpool FC will take on promoted side Cardiff City in their next Premier League fixture at Anfield on Saturday.
Fabio Aurelio: Signed in free transfer from Valencia in 2006. Sold to Gremio.
Lucas Leiva: Signed in £5m deal from Gremio in 2006. Sold to Lazio in 2017.
Diego Calvaleiri: Signed in £3m deam from Palmeiras in 2008. Sold to Cesena in 2010.
Doni: Signed in free transfer from AS Roma in 2011. Sold to Botafogo in 2013.
Philippe Coutinho: Signed in £8.5m deal from Inter Milan in 2013. Sold to FC Barcelona in £120m in 2018.
Roberto Firmino: Signed in £29m deal from Hoffenheim in 2013.
Fabinho: Signed in £40m deal from AS Monaco in 2018.
Alisson Becker: Signed in £67m deal from AS Roma in 2018.
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