Sadio Mane of Liverpool celebrates after scoring his team's second goal during the Premier League match between Liverpool FC and West Ham United at Anfield on August 12, 2018 in Liverpool, United Kingdom.
Klopp said the team needed to improve at both ends of the pitch if they are to make a genuine title challenge and not end up as last season - finishing fourth 25 points adrift of City.
After last year's second successive top-four finish and thrilling run to the Championship League final, big things are expected of Liverpool this time around.
"We played as good as possible today and we extended a really good pre-season into the Premier League", Klopp told the BBC.
"I know that Salah was [thought] a good deal for Roma, but now people say it is a good deal for Liverpool".
'Look, after six weeks I don't make the difference between a new player and other players because for me, it's exactly the same performance if Mili [James Milner] and Gini [Georginio Wijnaldum] are ready to make the next step in their development as well. "We are the ones who have to do more and fight more - that must be our attitude".
Unai Emery takes positives from Arsenal's second-half display
The game against City will be Arsenal's first in the Premier League without Arsene Wenger as manager since September 1996. He played also good in the preseason, but he can wait for his moment to arrive".
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"West Ham will play a good season but they are not the (Manchester) Uniteds or (Manchester) Citys".
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Mane's second should have been disallowed for offside but that was the only complaint West Ham could have about the result, with Manuel Pellegrini's expensively-assembled side looking a long way from settled.
Mane, who has now scored in each of his last three Premier League openers, and Salah, the league's Golden Boot victor last season with 32 goals, sealed Liverpool's victory in their first competitive game since they lost the Champions League final to Real Madrid in March.
A revelation in his first season at Anfield with 44 goals in all competitions, Salah is now a marked man. Mane, Roberto Firmino and Salah were just too good for West Ham while the sight of Sturridge returning to notch his first goal since November 2017 could potentially be a significant boost for the rest of the campaign.
Lovren sat out the West Ham game and missed a large majority of Liverpool's preseason after being granted an extended break for helping Croatia reach the World Cup final. LFC Globe will bring you the latest from Anfield with our match-day coverage.
Coming up against MFS presents an enormous challenge but as it is the first game of the season I feel like we can learn a lot from playing against such a fluid and unsafe front 3 and take what we have learnt from that into the rest of the season.