With Arsenal having moved to within a point of the top four with a win over Stoke City on Saturday, the pressure was on Jürgen Klopp's men to deliver at the London Stadium the following day.
But they acheived a crucial victory in style thanks to Philippe Coutinho's double and goals from Daniel Sturridge and Divock Origi.
Speaking after the game, Lallana revealed that there was a mood of confidence and not anxiety behind the scenes ahead of the game - a fact he believes is a great credit to his colleagues.
“It was a very calm atmosphere actually [in the dressing room],” he told Liverpoolfc.com.
“People were obviously talking about the pressure with the results on Saturday, but I felt very calm even in the warm-up and the dressing room.
“I felt the balance was right and we didn’t have to put too much pressure on ourselves. You only have to look at the teamsheet and it had goals, creative players, it had everything really, and I felt we trusted that, we trusted our ability.
“We had to be patient in the first half and obviously [Andre] Ayew had a big chance on the brink of half-time, but in the second half we came out of the blocks brilliantly and probably if it wasn’t for their goalkeeper we could have had a few more.
“People may say West Ham didn’t have much to play for and they made a few changes ahead of the game but we were without players as well in Jordan Henderson, Sadio Mane and Roberto Firmino, so we were missing big players, as we have all season.
“Credit to the lads today. It was a big pressure game but the way we dealt with it was superb.”
LFCTV GO: Lallana discusses Reds' win over West Ham
Lallana also singled out Coutinho and Sturridge for special praise over their role in a phenomenal attacking display in the capital.
“Philippe was on fire today, especially in the second half - he was ruthless,” he added.
“He’s a big game player and he came up trumps in big moments for us. It’s a pleasure to be on the pitch with him.
“It’s also important we mention Studge [Sturridge]. He got the first goal and showed a calmness and [produced] a great finish after taking the ball around the goalkeeper. It was a big moment for us, that.”
Victory over Middlesbrough at Anfield on Sunday will secure a top-four spot for Liverpool, and Lallana has backed the team to get the three points in front of an expectant Kop.
“I’m fully confident,” he said. “We are at home and it’s important that our fans play a big role for us.
“Nothing is going to be sealed in the first 20 or 30 minutes, we need everyone to be patient and just trust the team, trust us and it’s in our hands so we’ve got no excuses really. I’m confident we are going to win and seal that fourth spot.”
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Liverpool’s No.20 believes securing a return to Europe’s elite competition would represent a good season for the club, especially considering the injury problems that have kept key players on the sidelines at crucial times.
He added: “You just have to look at how the league has been so challenging this year.
“Obviously, Chelsea have won it comfortably in the end but the battle for fourth spot has been very exciting and there have been five or six teams challenging for it.
“The top four will be a successful season for us if we can make it, although people will think we should have had a bigger hand in challenging for the league, but for one reason or another we have been missing players throughout the season.
“It will be important we add to the squad [in the summer], bolster the squad just in case of injuries and suspensions.
“There are going to be more games next year, but we’ve achieved nothing yet and we’ve still got another huge game next week so it’s important we focus on that.”