'We fight for everything': Klopp salutes Liverpool's perfect start
Klopp's side made it six successive league wins to open the season as they survived a second-half Chelsea barrage to move five points clear of Manchester City.
Trent Alexander-Arnold's blistering free-kick and a Roberto Firmino header put Liverpool in control before N'Golo Kante's superb second-half strike set up a tense finish.
Liverpool managed the pressure-packed situation with the kind of mature, well-drilled display that is the hallmark of champions.
And Reds boss Klopp insisted he never doubted his players would thrive under the cosh because they are such a committed group.
"I shouldn't be surprised anymore by the character of our team. We expect it from us that we fight for everything," he said.
"The boys did really well, they fought really hard. It is completely normal that you come under pressure but we defended well. That is how it is in the top six and in the Premier League. You will never win at Chelsea without putting a proper shift in and we did that today."
After City's astonishing 8-0 demolition of Watford on Saturday, this was the perfect response from Liverpool as they try to dethrone Pep Guardiola's champions.
Chasing a first English title since 1990, Liverpool are on a club-record run of 15 successive league wins and have lost just once in 45 top-flight matches, going unbeaten in the last 23.
"It is exceptional. What can I say? We have to keep on going. It is never looks as easy as it did for City yesterday but we have not had these games yet. We have to work for it," Klopp said.
"We knew how good City were before the game yesterday. I really believe they are the best team in the world. They are brilliant. We are not bad as well. We have to be ready for each opponent. They are want to give us a knock, rightly so."
- 'Character and spirit' -
The only worry for Klopp was an injury to Senegal winger Sadio Mane that forced him off in the second half.
"It is a knock on the bone around the knee and a dead leg," Klopp said.
"He's OK, but we took him off, he wasn't limping but I didn't like how he was running."
Chelsea had a greater share of possession, managed 13 shots to Liverpool's six and won six corners to their opponents' four.
But those encouraging signs were undermined by poor defending and a lack of cutting edge, leaving Lampard as the first Chelsea manager to remain winless in his first four home matches since Bobby Campbell in 1988.
Lampard claimed Chelsea deserved more from their spirited effort, but he conceded his young side aren't mature enough yet.
"No home wins, we want to change that and I believe we will if we play like that," he said.
"Performance wise we were the better team. We had more energy in our game, character and spirit. That's why the crowd applauded at the end.
"The difference between us and Liverpool is we aren't consistent enough. To work towards those levels is hard. It is a daily thing. That is what we have to aspire to. The reality is younger players have come into the team."
Chelsea were denied a first-half equaliser when Cesar Azpilicueta's effort was ruled out for offside against Mason Mount and Lampard admitted it was a momentum changer as Firmino bagged the second goal moments later.
"I like to think we might get a couple in our favour. But you can see Mason is a tiny bit offside," he said.
"It changes the atmosphere in the crowd, on the pitch. We are slightly deflated and they get a boost."