Liverpool, in 10th place with 10 points after eight games, are enduring their worst start of Klopp's seven-year reign and with second-placed Manchester City set to visit Anfield next Sunday, there is little time to put things right.
"We don't have to look yet at the table but we know where we are without looking at it, so we are not done," Klopp told Sky Sports after his side's second defeat of the season.
Those two losses and four draws have left Liverpool trailing in the wake of Arsenal and City and though Klopp is frustrated by his side's slow start, he is not looking for excuses.
"This game (against Arsenal) is gone now, we cannot just accept a situation and say it's just not happening or whatever, we're not kids," he explained.
"We did a lot of good things, scored two really nice goals and played really good stuff against the team in form in the league, because we are probably the team not in form in the league."
Klopp's side face a quick turnaround as they visit Rangers in the Champions League in midweek before welcoming City and their free-scoring striker Erling Haaland (21) to Merseyside next weekend.
Asked what he would be doing to lift his side ahead of those two matches Klopp said he would be getting back to basics.
"Working, talking, thinking probably first, and then talking to the boys, and then coaching them and helping them, and then we go again," he said.
