The Uruguayan made it four goals in his last four starts when he headed home the Reds’ second of the night during Wednesday’s 3-0 win at AFC Ajax in the Champions League.
Nunez was also on target against Arsenal, Rangers and West Ham United during a productive October so far – and Klopp is confident the 23-year-old’s development will continue following a difficult beginning at his new club.
“Of course, it’s a massive step but the problem is not the boys need extra-long to settle or whatever, there are different situations for the specific players,” the boss explained during his pre-Leeds United press conference.
“Darwin came here after a short break in the summer, arriving in Asia, didn’t speak a word [of English] and then being young, Liverpool is a big club, it is a big step for him and he was expensive and all these kind of things. Then all of a sudden, you play the first game and everybody is looking at you. It's like the whole place is dark and there is only one light and it's the spotlight on you. You have to deal with that - we all expect them to deal immediately with it, [to] be prepared, but it’s not like this.
“That's the start: trying to get fit step by step with new training - with new, different things in training - different demands and all these kind of things.
“Then you start pretty well against City, coming on and scoring an important goal. The next game you score at Fulham and then you have a red card [against Crystal Palace]. He felt embarrassed for himself that he did that, definitely, like everybody would react like this.
“Then, from not being 100 per cent confident, getting a knock like this is not cool, which you can blame nobody else for because you did it and nobody else. Then you have to start new.
“For all these things, his numbers are incredible to be absolutely honest. If you speak about xGs, I am pretty sure his xGs are pretty high as well. He had a few chances which he missed, but he scored as well. He is involved in a lot of finishing moments, a lot of things.
“The steps he's making are really big and that means automatically that he settles in more and more.”
Overall, Nunez has netted six times in 13 appearances for Liverpool so far after arriving from Benfica in June.
Asked just how good the No.27 could become for the Reds, Klopp replied: “Nobody knows, he doesn’t know. Nobody knows, there is a lot [of potential] and it is so exciting, but he has to stay fit, he has to be available all the time and he wasn't against Nottingham Forest [last weekend].
“That's all important in the life of a professional football player. We have to work on all in all different areas. Then, the potential is incredible. It's not only speed, the attitude is really good, he is a real worker.
“Again, I tell you - and I know there are some people out there who think, 'Technically, not sure, first touch...' - it is incredible. That he doesn’t bring it on the pitch all the time, the first touch might be here or there sometimes, is nothing to do with technique. It is just a bit too late, awareness, orientation and all these kind of things, but it is all possible to develop and to learn.
“That’s where we are at, it’s really exciting, but where it can go I have no idea.”