The Reds brushed aside a youthful Gunners squad with ease at Anfield. While the scores remained 0-0 at half-time, both managers were embroiled in a heated exchange following Sadio Mane's aerial challenge on Arsenal right-back Takehiro Tomiyasu.
Arteta called for Mane to be booked which angered Klopp who didn't think his star deserved a card. When pressed on what went down, Klopp said: "It wasn't the plan - the situation was that Sadio [Mane] goes for a clean heading challenge, no one makes a foul and they get up and for me it's a bit too obvious that there was nothing.
"He's just a physical player - you can't do that, it happens too often and it's not right. When they rise up from the bench it's difficult to not get up and say something."
He added: "It was about the situation that it was no foul from Sadio [Mane] but the Arsenal bench went up like it was a red card. I asked what they want in that situation.
"We had to take Sadio off against Atletico [Madrid in the Champions League] because they wanted him to get a yellow card. The referee did really well in that situation - I deserved a yellow card. It wasn't not OK and that is what I said. It just happened in the moment.
"If it was a harsh challenge we are all like this, but it was nothing, he didn’t even touch him, it was just two players going up in the air. And [Arteta’s reaction] was not okay and that is what I said."
Speaking after the game, Arteta denied that the spat between him and Klopp had any effect on the game and says the pair had a discussion after the match.
"He was defending his team, I was defending my team, that's it. It doesn't matter," he said. "Yes I did [speak to Jurgen Klopp after the match] and I congratulated him. These moments are left on the pitch.
He added in a press conference: "I think the atmosphere was incredible from the beginning. That was it."