Sadio Mane's header and a screamer from Mohamed Salah in the second half were enough for Liverpool to see off Chelsea, who were hoping to derail their rivals' title hopes in a similar manner to their 2-0 victory at Anfield in 2014, when Demba Ba capitalised on Steven Gerrard's notorious slip to score.
At one point in the second half, Chelsea failed to convert a dangerous attack sparked by a similar slip from Andy Robertson, and Klopp claimed the incident should draw a line under Gerrard's error.
"At this point, we can finally close the slipping book -- Robbo slipped and nothing happened, so it's not a Liverpool thing," Klopp said. "Done. All good.
"I am so proud of what the boys did, and I loved, loved, loved the atmosphere -- it was outstanding what the people did. You could feel it, they are all on their toes, so let's try to do that seven more times and then we see what we get for it."
Three days after video surfaced of a group of Chelsea supporters aiming a derogatory chant toward him on social media, Salah hurt his former club by smashing a left-footed shot into the top corner from 25 yards to double Liverpool's lead.
"It blew me away," Klopp said of Salah's goal. "I was really happy. I saw it really well; maybe I saw it first the ball would go in. It was a really, really outstanding finish. And I don't want to minimise that but I loved the first goal exactly the same.
"It immediately reminded me of the 4-3 against Borussia Dortmund, only Hendo [Jordan Henderson] instead of Millie [James Milner] and Sadio instead of Dejan [Lovren], but a similar situation with this wonderful cross in that area and really good team play.
"The performance was really good, but to really make it happen you need the goals and we got them, all good."
Liverpool sit two points clear at the top of the Premier League from Manchester City, but Pep Guardiola's men can return to the summit by winning their game in hand. Klopp knows his team are not ultimately in control of their title destiny, but he remains determined not to focus on developments at the Etihad Stadium.
"The biggest challenge for us is always facing the world outside -- you [journalists] and other people -- because we don't think like that," he added.
"They [City] win [against Crystal Palace] and [did it] ask a question for us? If we think about them, yes, and if we don't think about them, no. We play our game.
"If, for example, City lose and we know it five minutes before our game, somebody tells us, 'City lost,' that's not a help. Then you lose your focus in that moment. What we want to do is collect as many points as possible, really -- 85 points, four games to play, that means [we can get] 97.
"Good, let's try. Let's try that. If that's enough, perfect, and if not, we cannot change it."