West Ham will take huge confidence away from a game in which they matched the Reds, before providing the killer blow when presented with the opportunity.
After all, Klopp’s side will either be there, or thereabouts, come the season’s end alongside both Chelsea and Manchester City – who will push them all the way.
On another day Liverpool might have won it themselves, but the Hammers proved to be the more clinical of the two.
As for Liverpool, dropping points against a well-organised West Ham is by no means a failure, but all those points add up in a title race.
But if Liverpool are to do what many tip them to do this season: be crowned champions, then Klopp will have to deal with plenty more fears between now and the end of the campaign.
The Hammers took the lead in peculiar circumstances when a fifth minute corner was turned into his own net by Alisson Becker.