Klopp's side have been tipped by many as the side most likely to challenge Manchester City for the crown, but the Liverpool manager is not getting carried away with one result.
"We know the expectations; we have expectations as well", he told reporters.
"People are not feeling that way about Manchester United or Tottenham or Chelsea at this moment in time, because of what has happened in pre-season". How can we be something different?
"In the first half we needed less respect for City and then more aggressive pressing", he said. That's what we spoke about and what we expect from ourselves. However, the linesman never raised his flag, much to the disappointment of West Ham's defenders. That's really hard but something we look forward to because you want to compete with the others and City are one of the best.
The strength of Klopp's squad was underlined by the Liverpool bench against West Ham, with Daniel Sturridge, Xherdan Shaqiri and Jordan Henderson all introduced in the second half, while Fabinho and Adam Lallana unused.
West Ham offered little as the hosts dominated, but Klopp was reluctant to describe the performance as flawless.
"It's a good way to start the season", he stated. The early signs are good on the basis of another free flowing performance full of pace and skill from the trio of attacking talents, who seem to compliment each other so well.
"We can not test the test before we have a test. For that it was a clear start, it was good".
Mane was on the score sheet again as he gave the Reds a 3-0 lead just minutes after half-time when he pounced on a through-ball from Firmino but replays showed he was offside.
But a devastating injury in the Champions League final left Salah unfit and Egypt eventually crashed out after three losses. "That's what we're going to try".
"As a manager you can work a lot of different ways with a lot of different tactics, a lot of different systems, but if you don't have good players it's impossible to be a good team". They deserved to win.
"I think it has to be normal, because that means you're a big club".
"We need to win our second game".
"If you want to compete with them you can barely drop points". I am not complaining.