Whilst a large proportion of Liverpool supporters are getting excited over the prospect of the league title returning to Anfield after 29 years, Klopp was keen to downplay the situation his team find themselves in.
"We cannot look too far ahead and we won't allow that to happen," Klopp said. "We were aware of the Tottenham result ahead of this game, but we can't allow that to affect us.
"The performance in this game suggests we remained focused on what we can affect and that is our own results. We haven't conceded a lot of goals this year so we didn't know how we'd react, but the response after Arsenal scored first was world class.
"We stayed clam and really forced the mistakes. Bobby's (Firmino) second when Sadio (Mane) won the ball. Wow. It was perfect defending, but we knew in the second half that the game wasn't finished so we wanted to control it.
"Mo Salah gave the penalty to Bobby and I almost cried because we all know how much Mo wants to score goals. It was really nice. Overall 5-1 against Arsenal doesn’t happen too often so I'm really happy with the boys.
"Now on to the next game. It doesn't matter how big the lead is in December. We will remember that."
Meanwhile, Arsenal manager Unai Emery admitted Liverpool's progress is an "example" for his side as he called on them to emulate the Reds' success.
"I think we started well with the first goal and then they had the difference with attacking moments, determination and quality. We couldn't stop this moment," said Emery.
"The second half we wanted to little by little impose ourselves to find one goal but another penalty closed the match. Bad result. This loss we can use to be better.
"We know we need to defensively get better. Liverpool have progressed a lot and it is an example for us. We need to do this progress."
Next up for the Reds is a visit of the Etihad Stadium on 3rd January, a fixture that is a huge opportunity for Liverpool to further the gap between their title rivals.