The result continued West Ham's awful record at Anfield, which now extends to one win in 46 league games.
"We played as good as possible today and we extended a really good pre-season into the Premier League", Klopp said.
Just under three months ago, Liverpool were at Anfield terrorising Brighton on their way to a 4-0 victory, and the offseason has seemingly done nothing to slow them down. Naby is in because he's a really good footballer.
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.
It was a chastening start to the season for West Ham as Liverpool's forwards consistently tore through their high defensive line.
Raheem Sterling and Bernardo Silva spoiled the Premier League debut of Arsenal manager Unai Emery as Manchester City opened the defence of their title with a 2-0 victory at the Emirates Stadium.
Brazilian midfielder Fabinho was one of Liverpool's marquee summer signings but he was left on the bench for the home match against West Ham on Sunday.
'It's a different playing style than at Monaco; there were two of us in midfield there and here at Liverpool there's three.
What we can not do is get carried away and start thinking the good times are rolling again at Anfield because despite all the optimism around this team, they have won nothing yet. The player is now in the final year of his contract and could still leave Anfield next summer but for the time being at least, it now appears as if one of the most talented strikers in recent Premier League history still has a part to play.
"I think Liverpool played better than us".
The Senegalese forward added his second and Liverpool's third early in the second period. "We have to be ready week in week out for the challenges", he said.
Naby Keita's presence has enabled Liverpool to alter their attacking shape a bit.
He made the headlines this weekend for the right reasons, scoring the team's 4th goal in the opening game of their 2018/19 campaign against West Ham, with his first touch after coming off the bench late on.
City strike fear into their rivals and that aura allows them to take control of a game from the first whistle, with the opposition rocking back and waiting tog get beaten.