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.
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.”
Sturridge, back in the starting line-up in the Premier League for the first time since January 2, raced onto Coutinho’s exquisite through-ball to open the scoring.
Yet Liverpool had an extraordinary let-off on the stroke of half-time thanks to an astonishing double miss from Andre Ayew, who hit the post twice from two yards out.
West Ham caved in after the break and Coutinho twice weaved his way through to make it 3-0 before Origi tapped in a late fourth.
It was not the way the Hammers wanted to end what has been a turbulent first season as tenants of the former Olympic Stadium.
The five-match unbeaten run which steered them clear of relegation trouble came unceremoniously to an end and a ‘lap of appreciation’ by the players was conducted in front of virtually empty stands.
“I am very disappointed the way we played,” said manager Slaven Bilic. “We wanted to put in the same performance as against Spurs, but it wasn’t to be.
“We have to be honest about it. We wanted to avoid that factor of complacency but obviously it was there, at least sub-consciously.”