Klopp's side have been tipped by many as the one most likely to challenge Manchester City for the title.
As he was quick to point out, the clean sheet was just as pleasing as his side's attacking play.
"There must have been something in the water among the Premier League's left-back fraternity this weekend as also breaking double figures was last season's Jose Mourinho bête noire Luke Shaw". That's what we expect from ourselves and then we will see where it leads because West Ham will play, for sure, a good season.
"After six weeks in I don't make the difference between a new player and another player because for me, it is of similar importance to Millie [James Milner] and Gini [Georginio Wijnaldum] are ready to make the next step in their development as well". He can keep the ball and give us - I don't want to say time to rest - but time to keep the ball as a team.
To many, Naby Keita was an unknown quantity of sorts heading into his first competitive 90 minutes as a Liverpool player against West Ham United on Sunday.
The champions, attempting to become the first team since Manchester United in 2009 to retain the title, were too good for an Arsenal side playing under new Spanish manager Unai Emery.
He was initially installed as a ball-carrier in midfield while the duo of Georginio Wijnaldum and James Milner kept things settled in midfield.
Man United vs Leicester City, Premier League
If Harry Kane can pick up where he left off from the World Cup, they should pip the other two London powerhouses for fourth spot. On Sunday, bigspending Liverpool will open their account when they host West Ham .
City showed just what a task overturning a 25-point deficit last season will be for Liverpool in outclassing Arsenal in a 2-0 win at the Emirates despite a far more disrupted preparation for the campaign due to the World Cup commitments of most of their squad.
"He has a lot of help from the players around him: Sadio works really hard, same with Gini and Milly and Robbo (Andrew Robertson)".
Liverpool won with four goals to nothing.
"We knew we played against one of the best teams in the Premier League".
Pellegrini continued: "We concede in the first half and then had two or three clear chances to draw level, then conceded in the last second of the period so we arrived in the dressing room and it was tough".
The second goal, however, was asking for an offside decision but it was never called and the Senegalese attacker made it 3-0.
'But there does seem to be a definite threat from Liverpool at this moment in time, but Liverpool will have to prove that'.
West Ham: Fabianski, Fredericks, Balbuena, Ogbonna, Masuaku, Noble, Rice (Snodgrass, 46 mins), Antonio, Wilshere, Felipe Anderson (Hernandez, 62 mins), Arnautovic (Yarmolenko, 67 mins).