The Reds bounced back from the disappointing defeat to Leicester City earlier in the week with Roberto Firmino and Sadio Mané putting the home side well in command by half-time with well-taken efforts.
Despite Alexis Sánchez's half-time introduction sparking a second-half fightback, Danny Welbeck reducing the deficit, Liverpool sealed the three points in stoppage time after Georginio Wijnaldum expertly finished off a counter-attack.
Klopp delighted by 'wonderful' first-half performance
The German hailed his side as "absolutely spot-on from the first second in the game", adding that they had a "wonderful first-half" in a first-half in that it "was clear it would be very intense."
Klopp insisted that the intensity was obvious from even the line-up, explaining that while Mesut Özil and Alexis Sánchez were absent, the rest of their squad meant they "needed to have an eye on the counter attacks and all that stuff."
"Both teams tried to play high pressure. That was the reason for a lot of long balls, which made sense," continued Klopp, saying that both sides "tried to play football" after "winning the second ball."
He felt that his team "did better" in the first-half and "played really good, created wonderful chances and scored only two times" when they "could have scored more."
First five minutes of the second-half felt like 50, says Klopp after Sánchez's introduction
Klopp declared that "it was clear a response would come from Arsenal" after a poor first-half and that they would "especially" improve with Sánchez on the pitch - having been controversially benched by Arsène Wenger.
He labelled the Chilean winger a "world-class player" and said he is "completely different" to Danny Welbeck "for example", adding: "It took five minutes but they felt actually like 50, to adapt to the situation. They already had two big chances at the beginning of the second-half."
Klopp acknowledged that Liverpool "needed Simon [Mignolet]" as well as "a little bit of luck" in order to survive Arsenal's pressure, but praised how his side "controlled the game then again" and then had "a chance for a counter-attack" late on when the Gunners pushed on.
He declared that it was "really intense" but said: "They scored the goal after Firmino goes down in their box and we blocked the ball from Sánchez before we scored the third one. It was a long way to go for all the goals, it was very intense between these two boxes. It was good again."
Asked whether he expected his team to produce as inspired a reaction as they did at Anfield, Klopp admitted that if the same question was asked of him on Wednesday then "the answer would have been 'no'."
He added: "If you would have asked me on Thursday, I would have said 'not sure'. And then if you asked me on Friday, [then I would have said] 'yes we can'."
Klopp insisted that reactions "are not always the same" and that it was "not clear it would happen" against Arsenal, but regardless vowed that it "should not be a surprise because the boys have played already a few times like this."
Reds boss salutes relentless Adam Lallana
Klopp highlighted midfielder Adam Lallana's energetic performance, with the England international among the Reds' stand-outs with Mané, Firmino and Wijnaldum also all impressing.
The Reds boss said: "When we are compact, it is really nice to have Adam because he jumps out of compact formations and triggers the pressure or sets the tone."
He explained that they have had a few games when they have failed to be compact and Lallana presses then it "opens a gap for the opponent" and invites "a one-on-one in a big area" which he called "the problem."
Klopp hailed how his side were "as a group really compact" throughout, adding that "stability is the base for everything" and they "wanted to be stable", praising how the Reds "worked really well in these parts together" and how "it is nice to have him [Lallana] in this row."
The win took Liverpool back into the top-four, leapfrogging Arsenal to temporarily move into third although fourth-placed Manchester City - also on 52 points - have two games in hand.
Klopp cited the confidence that being in the Champions League spots will give his side after enduring "a really hard week" following the defeat at Leicester, calling what went wrong "pretty clear."
"Next day, we made the analysis, which was nothing to enjoy for me and not for the boys when they saw it. But there was a point in the week when we actually had to finish the Leicester game," he said.
Looking back on their disappointing performance, Klopp insisted it was "absolutely exceptional" because there were "so many bad individual performances" which made it "really difficult" to win.
Klopp: Liverpool are the rollercoaster team of the Premier League
Klopp called the manner of his side's display at Leicester "frustrating" and said: "We are kind of the rollercoaster of the league - a lot of ups and too many downs. But only if you are really silly then you let the bad things have more influence on you than the good things."
Instead, the manager insists Liverpool have to "remind ourselves of the good things" so that they are "ready to go again" - adding: "How you can imagine, when you make an analysis like this and watch training or have training and you see the training you think 'okay, that didn't help obviously in getting confidence back.' That's not the nicest moment. The weather was not too cool, it was rainy in training and then it was not clear that we will perform like we performed."
Klopp enthused that his team "showed again what they are capable of" and declared that he does not like "the fact that inconsistency is part of the deal in development."
"Usually you win games and you lose against the big teams because at the beginning, when they are at a higher level, they are smarter and more experienced and you lose the games," he said. "We've chosen another way but it's still part of the deal and we know that we have to keep on going, and we will."
Klopp was also asked whether Wenger's decision to drop Sánchez in favour of Giroud surprised him, but declared having been "17 years a manager" that he is "really not surprised about any line-ups."
He admitted that their pre-match analysis was done with Sánchez in the line-up, but said with Giroud on then it became a "different game because they cross more often."
He declared that, despite Sánchez's obvious quality, it was "not a big advantage" that he wasn't playing to start with because he "had a big impact on the game" off the bench and they "had to adapt to it" whereas they "could have already [had] a better solution from the beginning" if he had started.