Manchester United will be back in action in next season's Champions League after they hammered Chelsea 4-1 on Thursday to secure a top-four finish in the Premier League.
Casemiro, Anthony Martial, Bruno Fernandes (penalty) and Marcus Rashford scored for United, who needed a point from their final two league games to officially end Liverpool's fading hopes of securing a spot in Europe's premier club competition.
"It's important, this club belongs in the Champions League," manager Erik ten Hag told Sky Sports. "But it's not easy in the Premier League, it's a tough competition, so it's a massive performance when you get this done."
Three-time European champions United, who failed to qualify for the Champions League last season, are third on 72 points with one game remaining, six points clear of fifth-place Liverpool.
Fourth-placed Newcastle United secured a spot among Europe's elite following a goalless draw against Leicester City on Monday. Chelsea, who have struggled all season, are 12th with 43 points.
United, who cap their Premier League season on Sunday by hosting 10th-placed Fulham, won the Carabao Cup in February and will be aiming to complete a domestic double when they face rivals Manchester City in the FA Cup final on June 3.
"(The season has been) decent, it's not perfect because we want more," Fernandes said.
"But for what we did this season, I think it's great. "Won one trophy, we get to the top four, that was our goal after we saw we couldn't go for the Premier League (title).
"Now it's about finish the league well and go to the FA Cup and win."
Ten Hag's side are unbeaten in Premier League action at Old Trafford for 17 games, going back to the opening weekend of the season.
"They know how important they are for us," Fernandes said of the home supporters. "You could see during the season how important it was in many games, so we just appreciate all the effort."
Casemiro scored in the sixth minute with a close-range header off a long free kick. The Brazilian helped set up Martial's goal just before halftime with a no-look chip into the path of Jadon Sancho. Martial was there to slot the ball into the empty net.
Interim manager Frank Lampard's Chelsea side collapsed in the dying minutes. After Fernandes had made it 3-0 with a penalty in the 73rd minute, Rashford returned from a two-game absence to score his 30th goal of the season, cutting the ball around keeper Kepa Arrizabalaga.
Joao Felix pulled one back for Chelsea in the 89th minute.
The one negative on the night for the home side was the loss of Antony, who was left in agony with an apparent foot injury and had to be carried off on a stretcher. Ten Hag said he did not yet know the extent of the injury.
Liverpool miss Champions League spot
Liverpool forward Mohamed Salah said he was "totally devastated" that they had failed to secure Champions League qualification and that the club had let the fans down.
Manchester United's 4-1 win over Chelsea on Thursday ended Liverpool's hopes of earning a berth in Europe's premier club competition next season. Juergen Klopp's side are fifth, four points adrift of the top four with one game remaining.
Last season, Liverpool finished just a point behind Premier League champions Manchester City but failed to mount a challenge in the current campaign due to injuries and a run of poor form.
"I'm totally devastated," Salah said on Twitter. "There's absolutely no excuse for this. We had everything we needed to make it to next year's Champions League and we failed.
"We are Liverpool and qualifying to the competition is the bare minimum. I am sorry but it's too soon for an uplifting or optimistic post. We let you and ourselves down."
Liverpool play at Southampton in their final game of the season on Sunday.