It put Slaven Bilic's side right back in the race for Europe in this most open of Premier League seasons.
Meanwhile, Liverpool are languishing in eighth place after being tipped for a title tilt just a matter of weeks ago.
Klopp tried to deflect criticism by claiming the Reds should have been given a foul before the East Londoners' first goal.
'They battered Liverpool'
But BBC pundit Shearer, who scored 313 goals in 622 career games for club and country, told Match of the Day Bilic's side were fully deserving of the victory.
"They thoroughly deserved the points and should have scored more goals.
"Yes the first goal was a free-kick (to Liverpool) but there was still a hell of a lot of work to be done.
"Antonio showed great attitude and desire to put the tackle in at one end and runs up the other and gets into the box.
"That's what (Christian) Benteke needs to be doing and the Liverpool players and staff need to realise that too. If they are going to get the best out of Benteke they need to get balls into the box."
Don't make excuses Jurgen
Klopp needs to be careful how he reacts to defeat during this period of transition for the Anfield side.
West Ham were by far the better side at Upton Park and Klopp would be better recognising that fact rather than making excuses for his side.
Meanwhile, West Ham are proving they will be contenders for the European places if they can keep their squad fit for the remainder of the season.
With the likes of Dimitri Payet making his comeback in the 2-0 win and the club putting together a seven game unbeaten run the Hammers are a club on the up.