The Guinean midfielder has taken time to settle since his arrival from RB Leipzig last summer, but Klopp was rewarded against the Cherries for picking him ahead of Jordan Henderson and Adam Lallana.
Per the Mirror's Simon Bird, Klopp said:
"There is still a lot to come, because he is still adapting. Sometimes it takes longer, that's how it is. People lose patience, that's normal. But we don't. You have to talk and explain. For a boy or a young boy—he turns 24—he made a big move from Leipzig to Liverpool; he wants to do it right.
"Against Bournemouth, it looked natural. That's exactly where we wanted it to come and where we wanted it to go. It was the big step he needed.
"We have a lot of options. Hendo maybe could have played. Adam could have played again. But it was clear that Naby was pretty much one of the first on the teamsheet."
After Sadio Mane opened the scoring from a James Milner cross, Andy Robertson played in Georginio Wijnaldum to score Liverpool's second after Keita helped regain possession from Jordon Ibe for the Reds on the left flank.
Keita played an even bigger hand in Mohamed Salah's goal to wrap up the three points, as it was his defence-splitting through ball that Roberto Firmino flicked into the Egyptian's path.
Football writers Leanne Prescott and Joel Rabinowitz singled out Keita, who turned 24 on Sunday, for praise after the match:
Leanne Prescott @_lfcleanne
Naby Keita much improved. Looked lively throughout, providing chances to the front three including a brilliant through ball to Firmino for the 3rd. Brighter off the ball too, working hard to win possession back. Really stepped it up a gear - central role is where he needs to be.
Squawka Football illustrated his heavy involvement in the proceedings:
While he may have struggled to hit the ground running at Anfield, Keita's performance offered a reminder of what an asset he can be when he finds his feet.
A dynamic and energetic box-to-box player, Keita works hard to win the ball for his side before looking to drive the team up the pitch.
While he's only been directly involved in one goal for Liverpool, he can make incisive contributions upon reaching the final third. During his two seasons with Leipzig, he produced 17 goals and 15 assists.
He's on his way to being able to have a similar impact for the Reds, and if he can maintain his form for the remainder of the season, he could play an important role in Liverpool's Premier League title challenge.