Klopp has hailed his players for standing up to the test at Burnley.
Jurgen Klopp saluted his Liverpool stars for their impressive performance after beating Burnley 3-0 at Turf Moor on Saturday.
The Reds were in second spot before the clash started because Manchester City had already thrashed Brighton 4-0 at the Etihad Stadium.
The Merseyside club secured a club-record 13th straight win, thanks to goals from Sadio Mane, Roberto Firmino and a Chris Wood own goal.
Following the triumph, Klopp, who was overly pleased with the attitude shown by his Reds, said there is still room for improvement.
"Very early when I came in, I told everyone that we want to create our own history and that is what the boys do week in, week out," Klopp told Sky Sports after Liverpool maintained their perfect start to the campaign.
'In moments we played really, really good football. Everything was there.'
"The intensity we put into games is unbelievable. I can ask for a lot but still the boys have to deliver, and they do.
"We were brilliant, there were so many 50-50 situations because of the long balls but we played early balls in behind as well. In moments we played really, really good football. Everything was there.
"We were a bit lucky with the own goal, but we forced that situation. We controlled the game as much as you can because Wood and (Ashley) Barnes fight so hard, and we defended it really well.
"We were aggressive but gave away no fouls, we worked our socks off. You have to show the respect for the opponent with the attitude you put in."
The German is hoping they extend their winning streak to 14 when they return from international duty.
"I didn't know before the game that we had 12 straight wins but now it's 13," the Reds boss added. "Newcastle are waiting on the other side of two international games for most of the boys.
"We want to have them all healthy back for what will be an unbelievably intense run of five away games and one home game.
"We have a lot to travel and a lot of things to do, but if we play like today with the same attitude, we have a good chance to win more games."
Liverpool lead champions Manchester City by two points after the first-four league matches.