Liverpool produced a superb performance at the home of their city rivals to record their third straight Premier League win and hold onto third position on the table.
Skipper Jordan Henderson gave the visitors the lead in the 9th minute and the former Sunderland man turned provider for Mohamed Salah ten minutes later to establish a two-goal lead before Demarai Gray halved the deficit before half time.
Salah got his second after the break and Diogo Jota sealed the win for Klopp’s men with his fourth goal in three games.
"It was a really good game from my team, a really mature performance, grown-up performance, much better than in years before, especially at Goodison," Klopp told Amazon Prime Video post-match.
"We were much too open when we gave away the goal but it can happen when you are superior. We should have been one or two-nil up before we scored the first goal.
"We scored the goals at 2-0 and maybe then we were not that ruthless, we gave them so life back. I am not seeking for perfection, if it would be easy I know everyone could do it. The boys did well."
Salah’s brace took him to 13 league goals for the season but Klopp revealed the Egyptian was unhappy not to have recorded a hattrick.
"He [Salah] was angry after the game!," he added. "He wanted to score the third one. I don't take these things for granted.
"His second goal, you have to force these kinds of mistakes. Mo put Coleman under pressure to win that ball and from then on it is a good chance he will score.
"We have momentum but it was by far the best performance since I've been at Liverpool at Goodison. Before the game people told me that in derbies form or shape doesn't count, I see it totally different."