Although their goals owed plenty to the Hammers' awful defending - and, in the case of Mane's second, an extraordinarily poor offside call - they looked slick, compact and risky from the first minute to the last. We will try to score more goals.
Yet Klopp admitted that he wasn't entirely impressed with Keita's displays last season.
"They were the better side in the first half and we think we were better in the second half".
Keita, meanwhile, combined industry and incision during his 70 minutes on the left of Liverpool's midfield three.
Danish defender Jannik Vestergaard, signed by Southampton during the close-season, made a strong debut and the Saints defence looked well-drilled and solid.
Under Hicks and Gillett, perceptions of Liverpool as a club from the city but no longer belonging to it had become widespread. It was hardly what you would expect overall from a £36million signing.
And after the first round of games, Liverpool sit top of the table, sending a clear message of intent to City.
Last season has made Klopp's mind up on the position.
Let's not forget that three senior centre-backs were absent from the squad altogether, too, with Lovren having played in the World Cup final three weeks ago and Matip and Klavan struggling with injuries.
"It has to be normal at a club like Liverpool - a club that will always buy good players, even if they already have good players".
"It's just one of those things".
Neville does have one concern for Liverpool, though, with regard to their stamina this season.
The win over West Ham was Liverpool's 27th in the league, more than they have against any other team, while West Ham have only won once at Anfield in 46 league games.
If Keita can maintain this form in the Premier League then he could prove to be one of the signings of the season and could propel Liverpool towards a title challenge.
West Ham couldn't live with the Reds' constant interchanging, Roberto Firmino dropping deep as Salah tucked in, Alexander-Arnold and Robertson bombing down the flanks whilst Keita and Milner shifted the ball around midfield with grace and elegance.
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