Last time out before the international break the Reds lost their 26-game unbeaten run with defeat at West Ham but bounced back in some style by clinically taking apart the Gunners as their 10-match streak without defeat ended.
Sadio Mane opened the scoring late in the first half before the hosts ran away with it after the break as Diogo Jota, Mohamed Salah and substitute Takumi Minamino – with his first touch – all got on the scoresheet at Anfield.
“We had to show a reaction, that was clear, but the only problem was that we weren’t together for most of the time,” said Klopp.
“We scored to make it 1-0 and the first half was absolutely fine. But it was still not right and we had to change and we changed and controlled the game in the second half.
“It was a mix of a very mature performance, a very exciting performance with exciting moments and goals, great counter-press and finishing situations off. It was an impressive result.”
The turning point appeared to be the off-field incident between Klopp and Gunners boss Mikel Arteta who argued about Mane’s challenge on Ben White before being separated by their respective coaching teams.
Klopp said he was “sick” of the Senegal international being unfairly targeted by opponents.
“It was a completely clean situation: two players jumped in the air, no-one touched the other in a foul, the bench of Arsenal is going for it and I just asked ‘What do you want from that?’,” he added.
“There is no contact really and it looks like everyone wants a yellow card. I’m sick of the situation when everyone goes for Sadio.
“You might remember against Real Madrid (last season) he was completely taken out of the game against Real Madrid without doing anything.
“Against Atletico (earlier this month) we had to take him off and it is just not right.”
On whether he felt that incident energised the crowd Klopp said: “It was not the plan but if helped it was OK – but it won’t happen all the time.
“It doesn’t happen very often any more that I have arguments on the sideline.
“It was not the most controlled game but not the most exciting so maybe the crowd needed some help and it pushed the team again.”
Gunners boss Arteta, remembered here for his time as an Everton player, accepted his improving side were not in the same class as Liverpool.
However, he was annoyed with the mistakes which the home side punished so clinically, but did not feel his players cracked under the pressure.
“In the second half they (Liverpool) got some momentum and we threw it away in the first 15 to 20 minutes,” he said.
“We have given it away in very dangerous areas, not with pressure and with pressure, and we lost control of the game.”
On his team’s lack of experience the Spaniard added: “I don’t know, I’ve seen the biggest teams in the world come to this ground and collapse.
“They were better than us for 96 minutes and that’s the level. They’ve been together for six years and today you could see the difference from the moment we lost control of the game.”