The Reds continued their march at the top of the Premier League table as they beat Spurs on Saturday thanks to a first-half strike by Roberto Firmino.
It was a dominant display from Liverpool, who were by the far better side, although Jose Mourinho's side also had their fair share of chances on the break towards the latter stages of the game.
The result hands Liverpool a 16-point lead at the summit of the Premier League, but Klopp was left slightly disappointed by his side not being clinical enough.
"First and foremost the result is the most important thing. One team deserved to win and that was us," Klopp said.
"To win at Tottenham is pretty special. That the game wasn’t decided after 50-60 minutes was our fault. It was very intense for us.
"You can expect them to defend deep in this stadium, but it was 4-6-0 in the first half. If it was easy to win here, a lot more teams would do it.
"I’m over the moon about the result, but we have to talk about the performance. We should have scored more goals – that’s the truth. We have to be honest with ourselves.
"We could have scored more and we have to – especially in this stadium against a team like Tottenham."
Klopp was clearly not overjoyed with the performance, but with the Reds just coming through a busy festive period, tiredness certainly played a factor on Saturday.
"We were on the ground towards the end and they were coming forward," Klopp added. "The spell we’ve had, it costs you rhythm.
"In the second half a couple of our players were slightly exhausted, but we fought through that.
"We played super football in their box, but for 90-95 minutes you have to be ready. We were, but we still have to do better.”
The result saw Liverpool set a historic record, with their 20 wins from 21 games representing the best-ever start to a league campaign in Europe's top five leagues.
“It’s special," Klopp said of the Reds' new record. "To win the number of games, to always be ready to fight, that’s what the boys to.
“The only thing is that you don’t get anything for best starts. The only thing we’re interested in is what we can get in the summer. This league is so strong. We have to be ready.
“Our lead is really not interesting. The moment we have so many points that nobody can catch us anymore, that’s when I’ll be interested.”