Liverpool, meanwhile, have not conceded a goal in their last six home games in the league - since West Ham scored against them in February.
"He's a very positive and motivating player, so this month has been very good and I've spent a lot of time with him".
Liverpool took their bright pre-season form into the new Premier League year but Klopp knows there is still room for improvement for the rest of the season.
West Ham offered little as the hosts dominated, but Klopp was reluctant to decribe the performance as flawless. But as part of the entrenched 4-2-3-1, the Brazilian's task on Sunday involved tracking the pacy full-backs far more than supporting Marko Arnautovic in attack.
The former Manchester City manager said: "It was a tough game before the game, during the game and after the game".
"[It was] nice. An absolutely good performance, of course", he told reporters.
Just 8 minutes in to the second half the "Irons" defence was too tame in dealing with a piercing run from Roberto Firmino, who slid the ball through to Mane who decisively added his second on the half-turn.More news: Aubayemeng will be Arsenal’s biggest threat against City
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Klopp has overseen three Premier League openers during his tenure and his charges have beaten the opposition keeper 11 times in those.
The Reds begin their season with a tricky tie against a Hammers side that were unbeaten during pre-season.
"But I think a couple of balls decided the score". We went to finals.
It featured everything we've come to expect from a stellar Liverpool display.
A recent survey revealed Liverpool were the Premier League's unluckiest club last season, with decisions costing them 12 points.
What was immediately evident, even on the basis of these opening 90 minutes, was that Liverpool are a different - and better - proposition with new midfielder Naby Keita catching the eye.
"They are a huge club, they have had many great players". N'Golo Kante, Paul Pogba, Dele Alli, Harry Kane, Raheem Sterling, Romelu Lukaku, Eden Hazard: it was only four weekends ago that all of these players participated in the final games in Russian Federation, but they're already back and doing what they do best.
Liverpool's midfield provided the foundation to both scorch and stifle with Gini Wijnaldum controlling well at the base, while Milner was core to every facet of play and Keita exposed spaces the visitors knew nothing about until he weaved through them.