The £64 million signing scored Liverpool’s third goal in the 3-1 win over Manchester City, while his header brought the penalty when Mohamed Salah scored the second and the Uruguayan twice came close to finding the net on other occasions.
Nunez, who came on for Roberto Firmino, has had a mixed pre-season, scoring four times as a substitute against RB Leipzig but missing chances in other games.
Klopp feels he was unfairly criticised in matches when he was not fully fit but thinks Nunez will be buoyed by opening his Liverpool account.
“Definitely,” he said. “They are a special species, strikers, and everybody needs little positives and for strikers that means goals or goal involvements.
“Darwin even without scoring the third one [was good], but the goal obviously is the icing on the cake so I am really pleased for him. You could see on his face and on the faces of all his team-mates how happy the boys are for him.”
He was happy with the forward’s overall performance, adding: “Good, really good. We saw Darwin Nunez in dangerous situations. He used the spaces and finished well, too. It was clear that he will get better with time.
“Everybody gets judged on first sight, that is not helpful to anyone but it happens. We are patient and we knew he could do good stuff. I like his impact today and the impact from the bench was exceptional.”