The Reds ensured their destiny remains in their own hands in the fight for a top-four finish with a 4-0 victory at the London Stadium.
Liverpool travelled to the capital knowing any slip-up could hand the initiative to Arsenal, and faced a Hammers team who had dashed Tottenham's even loftier ambitions just nine days earlier.
But two goals from Philippe Coutinho, sandwiched by strikes from Daniel Sturridge and Divock Origi, ensured that victory over relegated Middlesbrough on the final day will take them back to Europe's elite next season.
"We have one more game and we will stay focused, 100 per cent," said Reds boss Klopp. "We know the situation and no one will underestimate the next game. That's how it is, part of this life is to handle pressure. I thought we did really well.
"We drew the last game against Southampton and missed a penalty, and maybe people thought we don't deal with pressure.
"But these players did and that's why we are in the position we are - 73 points is not a present, we have had to work for it."