Keita joined Liverpool for £52.75m from RB Leipzig in the summer but has failed to realise the sort of form that persuaded the Reds to sign him in the first place.
The Guinean has shown glimpses of what he is capable of, but looked horribly out of sorts in the draw with West Ham last week.
He has struggled more than any other signing the Anfield club has made recently, but was much-improved in the win over Bournemouth.
The midfielder played a part in all three Liverpool goals in what Klopp felt was a “really important” display.
“A big step,” the manager said of Keita’s performance.
“We have a lot of options – Hendo maybe could have played. Adam [Lallana] could have played again, but it was clear that Naby was pretty much one of the first on the team-sheet but for different reasons.
“The second half against West Ham was a big step, but nobody really realised it because nobody was happy with the game and nobody talked about this.
“Maybe people liked to talk more about the negative things from the first half with Naby.
“We will probably see a couple of bad halves from Naby in the future, that’s completely normal. But it was clear the whole week the second half was really important to him.
“There is still a lot to come because he is still adapting. Sometimes it takes longer. People lose patience. That’s normal, but we don’t.
“I’ve said it pretty much about all of the [new] players, we are really demanding. The boys have a lot to learn. I’ve said this, and you can look back on your notes, adapting to what we want always leads to a little drop.
“Today 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.”