At the end, a dejected Rob Edwards stood in front of the travelling fans and watched them sing their hearts out. Luton knew their relegation was all but confirmed after this defeat by West Ham, but nobody could dent their pride.

There is no shame in their inability to bridge the massive financial gap since last season’s promotion. They have given their all and it is impossible to find fault in Edwards’s management. The only real takeaway is that it would have been a remarkable achievement if Luton, whose inferior goal difference means their chances of catching Nottingham Forest are almost nonexistent, had managed to stay up given their shortage of elite quality.

Related: Nottingham Forest v Chelsea: Premier League – live

“I’m an emotional person and walking over to our supporters and seeing their reaction brought me to tears,” Edwards said. “I feel devastated, I didn’t want to let anyone down and I feel responsible. I thanked the players and staff, they’ve given me the best 18 months of my life.

“We’ve been on this amazing journey. We didn’t get relegated because of today. We had a difficult period for eight to 10 weeks where we were missing players. I don’t want to make excuses. In the end this league has been a bit too much.”

It spoke volumes that West Ham did not have to be at their best to ensure that David Moyes won his final game in the home dugout at the London Stadium. They had toiled before James Ward-Prowse’s equaliser. Luton had led early, only to crumble after being pegged back early in the second half. Tomas Soucek, a Moyes stalwart and one of the Scot’s best signings, soon made it 2-1 with a fine strike and George Earthy, one of West Ham’s most exciting youngsters, sealed the points with his first senior goal.

“It was a great way to finish here,” said Moyes. “A positive note, a young player scoring and a good result for us. I was emotional. I’ve been here four and a half years. Sometimes all you hear is negative stuff. It looks like the best part of 50,000 supporters stayed behind to show their appreciation.”

The mood was relaxed during the closing stages, the win confirming West Ham’s third top-half finish in four years. That said, it should be noted that their performance during the first half demonstrated why they are replacing Moyes with Julen Lopetegui. The attack was laboured, the midfield a cavernous hole and an immobile defence punctured when Albert Sambi Lokonga headed Alfie Doughty’s cross past Alphonse Areola after six minutes of Luton dominance.

Where was the marking? Or the pressure on the crosser? Nobody closed down Ross Barkley when he sparked the move by finding Elijah Adebayo. West Ham were too open and they were slow to respond to conceding their 71st league goal of the campaign. The best they mustered before the interval were wayward shots from Mohammed Kudus and Jarrod Bowen. Moyes expected the boos that greeted the half-time whistle.

Yet the manager drew a reaction from his players. Luton, who have won one of their past 16 games, faded after a limping Barkley made way for Jordan Clark. Poor though they were, it always seemed that West Ham would not have to raise their level too much to wear Luton down.

So it proved when Bowen raced down the right and flashed a cross into the six-yard box in the 54th minute. Thomas Kaminski saved with his feet but the ball hit Reece Burke and ran to Ward-Prowse, who scored with a venomous low shot.

Luton’s body language was telling. The shoulders were slumped and they soon trailed. Michail Antonio, Bowen and Emerson Palmieri all missed inviting chances before a clearance fell to Soucek, who whacked an emphatic volley past Kaminski from 20 yards.

• Download the Guardian app from the iOS App Store on iPhone or the Google Play store on Android by searching for 'The Guardian'.

• If you already have the Guardian app, make sure you’re on the most recent version.

• In the Guardian app, tap the Menu button at the bottom right, then go to Settings (the gear icon), then Notifications.

• Turn on sport notifications.

There was no sign of a comeback. West Ham poured forward, Kudus missing a sitter. Luton’s race was run. Kudus beat Doughty, wriggled to the byline and produced a cutback. Earthy, who had just replaced Antonio, was waiting to apply the finish. The 19-year-old had not played since suffering a horrible head injury on his debut against Fulham last month. He will have fonder memories of this cameo.