The Reds signed Fabinho from Monaco last summer from in a deal worth €45 million (£39m/$52m) plus bonuses of up to another €5m (£4m/$6m).
Despite his hefty price tag, Fabinho was brought along slowly at Anfield, making his first Premier League appearance on October 20, two months into the season.
Since then, the 25-year-old has grown into a key performer for Liverpool, having started six of the club's last seven league matches.
Fabinho was at the heart of Liverpool's 5-0 win over Watford on Wednesday, putting in a strong 90-minute performance in central midfield.
“Fabinho was really good for sure,” Klopp told the Liverpool Echo of the Brazilian's performance against the Hornets.
“It was one of his much better games. He had some spectacular moments - getting the ball, a little steal here or there, really good.
“Organisation wise, he was brilliant. Protection wise, he was brilliant. Football wise, he was really good. For sure, it was one of his top games.”
Klopp was asked what has changed for Fabinho since the start of the season and said: "He’s just feeling more natural in his position.
"He’s a very nice boy and a very smart boy as well. He wants to do everything right.
"A couple of things changed for him, intensity wise and tactical understanding as well.
"But he did not need that as much as he maybe thought. Sometimes you leave the boys a little bit to adapt naturally to it and not give them so much information. Some things happen then.
"Now, it’s no problem for him if we play with three, five, six or seven, whatever in the centre. That’s exactly what we wanted. That's where we are with Fabinho now and hopefully it stays like that."
Clinging to a one-point lead over Man City at the Premier League summit, Liverpool take on Everton on Sunday in the Merseyside derby.