The 23-year-old Uruguay striker, who could become the club’s record signing if all the elements of his £85 million summer deal with Benfica come to fruition, was introduced with 30 minutes to go and produced an impressive cameo.
But he also caused Ederson a few problems, drawing the City goalkeeper into a challenge which would probably have resulted in a penalty were it not for an offside flag in his very first attack and then forcing the Brazil international into a goal-denying save.
“It was good, it was really good. It is clear it will get better with time,” said Klopp.
“We live in a world where everybody gets judged on first sight and that’s not helpful for anybody but it happens constantly.
“In the first few games [of pre-season] we were not even close to the fitness level of today and then when he came on, we passed each ball for him to chase it and after the third ball he was completely killed and then everybody judged his first touches and these kind of things.
“It’s just a joke but we have to live with that, he will deal with it brilliantly. We are patient and we know he can do good stuff.
“We all know they are a special species, strikers. The other thing everybody needs [are] little positives. That means goals, or goal involvements.
“I think Darwin would have been fine even without scoring the third one because the penalty was Millie’s cross and his header.
“The chance he had before he did really well, but Ederson reacted brilliantly. The goal was obviously the icing on the cake, so really pleased for him.
“You could see in his face, you could see in the face of all his team-mates how happy the boys are for him and that’s a really good sign after that short period of time that he is with us.”
Nunez’s involvement proved crucial as after Liverpool took a deserved 21st-minute lead through Trent Alexander-Arnold’s shot which clipped Nathan Ake before going in via the far post, they were pegged back by an improved City after the break.
While £51 million summer signing Erling Haaland did not score, fellow new arrival Julian Alvarez did, forcing home a close-range effort after 70 minutes.
Haaland had few chances to shoot never mind score, although he will want to forget his late effort from six yards when he hit the crossbar when faced with an open goal.
“He had chances, two or three in the first half, and one in the end, and always is there,” was City manager Pep Guardiola’s assessment.
Of the Norway international’s glaring late miss, he added: “He is strong, another time he will put it in the net. It happened. It is football. He was there.
“He had another goal disallowed because the ball was over the line.
“He fought a lot and made the movements. It is good for him to see the reality of a new country and new league.
“He was there but today he didn’t score and another day he will score. He has an incredible quality and he will do it.
“He has had just two weeks, two weeks and a half, and I am really comfortable with what we are seeing since we arrived this season.
“I am not absolutely concerned. The reality is we have two or three months ahead of us. He is going to help us.”