The Reds failed to pounce on their numerical advantage as resilient Chelsea dug deep to secure a point on the road.
Both teams came into the game with hundred percent records in the Premier League and the intent of landing a mortal blow to one another.
It was the Blues who drew first blood through Kai Havertz’s header from Reece James’ cross on the 22nd minute of the game.
Chelsea could have scored more goals moments later but passed up numerous opportunities to extend their lead.
The visitors went down to ten men after James blocked Sadio Mane’s shot on the line with his hand. Mohamed Salah scored from the penalty spot to pull parity on the cusp of halftime.
Liverpool dominated the game from that moment until the final whistle but made little effort to snatch all maximum points.
"Our press in the first half was absolutely exceptional. Chelsea are dangerous in all situations and that's how they scored the goal. I think we all agree we could have defended it better,” Klopp told reporters after the game.
"Everything was enjoyable apart from the result. I saw two very good football teams. It was a great first half from us and actually a good second one because it's so tricky when you play against nine defenders and have to create and create.
"Could we have done better? Yes. But it's early in the season. "For sure we should have made more of the advantage. We have one point more than before so let's carry on.
"I think it was a clear handball. I was happy with the first half performance - even though we were 1-0 down. I would have loved us to have a bit more greed and determination. Apart from that I liked the game, I liked the atmosphere."
