Had they failed to gain maximum points at the London Stadium, the Reds could have given a boost to top-four challengers Arsenal.
They were up against a West Ham side who had effectively scuppered Tottenham Hotspur’s Premier League title ambitions earlier this month.
But two goals from Philippe Countinho, plus further strikes from Daniel Sturridge and Divock Origi saw Liverpool to a convincing victory.
Now a win against already relegated Middlesbrough at Anfield on Sunday’s final day of the season will ensure five-time European champions Liverpool return to the elite of continental football next term.
“People were talking about the pressure with the results on Saturday, but I felt very calm even in the warm-up and the dressing room,” Lallana told Liverpool’s website.
The England midfielder added: “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 team-sheet and it had goals, creative players, it had everything really, and I felt we trusted that, we trusted our ability.
“Credit to the lads. It was a big pressure game but the way we dealt with it was superb.”
Defeat ended a difficult first season at the former Olympic Stadium for West Ham, where fans are much further removed from the action than they were at the Hammers’ compact former home at Upton Park.
The Liverpool loss was not West Ham’s only thumping home defeat this term, with the east London side conceding five goals against both Arsenal and Manchester City, four to Watford and City (again), and three to Southampton and Leicester.
“In the last few weeks we’ve been doing well,” said Hammers defender Winston Reid.
“We tried our best and went out there to try and put on a performance. But sometimes you have days like that and unfortunately we’ve had a few of them this season.
“But we’ll move on to next season and learn from this season, especially at home.”