The £100million pair made their first appearances in a Red shirt, playing 45 minutes apiece in the 7-0 friendly win at Chester.
Keita, in particular, slotted in seamlessly after the break and created one goal with his counter-pressing.
Klopp said he was helped by the fact former club RB Leipzig play a similar style and it would take Fabinho longer to adapt as Monaco’s football was different.
Asked what the pair will bring to the side, the Liverpool manager said: “Quality. It’s all good. You saw Naby comes from Leipzig and knows the football philosophy as it’s a similar one.
“He’s very sharp in the challenges, very quick in mind in these situations of counter-pressing, his impulses look kind of natural, which is good. Monaco played a completely different style, so Fabinho probably needs a few more days.
“But he’s a fantastic football player, a good passer, his challenges are good, a proper defensive midfielder with the option of being a number eight as well.
“If you want to be a part of our squad then you need to be good and these two boys are.”
Liverpool led 2-0 at half-time thanks a double from Wales international Harry Wilson but after the break Daniel Sturridge, who looked fit and sharp, scored twice, with Ryan Kent, James Milner (penalty) and Danny Ings completing the scoring.
Goalkeeper Loris Karius also had his first outing since his disastrous Champions League performance, where he was responsible for two of Real Madrid’s goals – with the club subsequently learning he had suffered a concussion.
The German made one good save, deflecting Jordan Archer’s shot over the crossbar and then late on in the first half did well to claim a high cross one-handed under pressure.
“It was a difficult save but he made that and it looked good and the high ball it was difficult,” added the Reds boss. “Many goalkeepers would have dropped it and then everyone would have been ‘Oh that happened’ and it starts again.
“I need cool down the whole situation and play football and work on our weaknesses, use our strengths and everything will be good.”