Liverpool's destiny is in their own hands after a dominant display at the London Stadium and victory over relegated Middlesbrough next Sunday will secure a top four finish in the Premier League.
If Arsenal drop points against Sunderland on Tuesday, Liverpool will make it back into Europe's elite club competition before the last weekend of the season.
"Part of our life is to handle pressure, to ignore the bad part of pressure and to use the good part of pressure," Klopp said.
"We drew in the last game with Southampton, we didn't score with a penalty and maybe people say then: 'They can't deal with pressure.'
"I thought we saw really a convincing performance with no doubts about anything.
"But the first sentence the players said in the dressing room was: 'One more time. One more game.'
"We will stay focused 100 per cent, we know about the difficulty of the next game, nobody will go into this game and underestimate it one per cent."
Liverpool will be heavy favourites to beat Middlesbrough, but Klopp warned his players to stay focused.
"Middlesbrough have had a hard season, and it's hard in a season like this to enjoy football," he said.
"I'm pretty sure they'll want to enjoy football at Anfield, they'll want to try anything and that makes life difficult for us.
"If we can be as focused as today and as fluent and have as good movements as today, then it will be difficult for them."
Klopp hailed man-of-the-match Philippe Coutinho, who scored twice and created Daniel Sturridge's opening goal.
Divock Origi added the fourth goal but it was Coutinho who drew Klopp's most fulsome praise.
Often lost stationed out on the wing, Coutinho flourished at the tip of the diamond and he has now scored six goals in the last seven games.
"He was never a winger, he's always kind of a playmaker, it's not interesting where he's coming from, he needs to be at one point, in the decisive area in the middle of the park," Klopp said.
"He needs to be in shooting situations and finishing situations, that's what he did today. Obviously he did really well in this position."
Sturridge was another to shine, scoring his first goal since January 2 after an injury-hit season.
West Ham want to sign the England striker, but Klopp said: "He gives us options. His paced troubles teams and I thought his timing was brilliant."
West Ham ended Tottenham's title tilt in their previous match, but there was never a chance of derailing Liverpool's European bid.
"I wanted the same performance as against Spurs or similar," Hammers manager Slaven Bilic said.
"We didn’t do it. We have to be honest about it. We were without a few players but also against Spurs.
"We wanted to avoid complacency but it was obviously there at least subconsciously.
"They were better, we were nowhere near close enough. If you give time and space to players like Coutinho, Sturridge and Lallana they will kill you.
"That's exactly what happened. If you put that on a performance that was not good enough, it usually ends like this."