Sheffield United now face a rebuild in the Championship with the club in crisis on and off the field.
Moyes praised midfielders Tomas Soucek and Declan Rice for their contributing this season and added that both the players can make further improvements.
Premier League: Manchester City manager Pep Guardiola praises David Moyes, Carlo Ancelotti's 'Buddha life'
The Hammers were facing a relegation battle when Moyes took charge for a second time last season, but head to the Etihad on Saturday in fourth spot.
The Hammers' 3-2 win over Crystal Palace on Tuesday was their sixth successive victory in all competitions and lifted them into fourth place in the table and a Champions League spot.
Britain on Friday reported a record 1,325 deaths over a 24-hour period from people testing positive for COVID-19 as overstretched health services struggled to cope.
Chelsea enjoyed a strong start to the season before losses to Everton and Wolves checked their progress but the victory at the London Stadium lifts them into fifth spot.
West Ham manager Moyes said he was baffled as to why people could gather indoors to see the game, but not outdoors in a 60,000-capacity stadium.
Premier League: David Moyes to call the shots for West Ham in Sunday fixture against Wolves despite self-isolation
Assistant coach Irvine took charge of the League Cup tie against Hull and secured a 5-1 win but Moyes will be the man making the decisions this weekend.
Premier League: West Ham owner David Sullivan left 'depressed' by online criticism from fans over lack of signings
The signing of Czech midfielder Tomas Soucek, who spent the second half of last season on loan at the club, on a permanent deal for a reported $19 million has been West Ham's only business of the summer.
Premier League: Manchester United held by West Ham, need one point against Leicester to secure top-four spot
The point was enough to secure top-flight survival for West Ham who moved up to 15th place on 38 points — four points above 18th-placed Watford.
Premier League: Ole Gunnar Solskjaer reaping rewards of time, patience at Manchester United, says former manager David Moyes
Moyes, who replaced long-term United manager Alex Ferguson in 2013, was dismissed after only 10 months in charge but the 57-year-old said he was looking forward to returning to his former side for Wednesday’s clash.
Premier League: With win over Watford, West Ham boss David Moyes proves yet again he's a man for crisis
Friday’s 3-1 home win over Watford should be enough to ensure the Hammers remain in the top flight — and this time Moyes will surely be shown more gratitude by the club’s owners.
Premier League: West Ham United take big step towards safety with win over Watford in relegation battle
The result leaves Watford just three points above the relegation zone, and facing daunting remaining matches against Manchester City and Arsenal.
Noble, who made his debut for West Ham in 2004 as a 17-year-old, will make his 500th appearance for the club currently managed by David Moyes if he plays in the upcoming fixture against Watford.
Premier League: Troy Deeney keen to be part of Watford's fight for survival despite knee issue, says Nigel Pearson
Troy Deeney, who underwent knee surgery at the start of the 2019-20 season, has featured in every match since the restart and has committed himself to helping his team fight for Premier League survival.
West Ham United manager David Moyes hit out at the Premier League schedule after his side’s relegation fears deepened with a 2-0 defeat at Tottenham Hotspur on Tuesday.
All 20 Premier League clubs on Thursday approved a range of matchday protocols for the season’s resumption but Moyes says there are lots of questions that still need to be answered.
Coronavirus Outbreak: West Ham United manager David Moyes says clubs facing financial crisis should rethink the way they operate
Football in England was suspended indefinitely last month due to the coronavirus and West Ham are among several Premier League teams to announce player wage deferrals to help their clubs cope with the financial impact
West Ham United became the second Premier League club to announce wage deferrals for their players to cope with the financial challenges posed by the coronavirus pandemic.
Premier League: Liverpool sway past West Ham after putting in 'normal performance' to stretch unbeaten run
While Liverpool have amassed a whopping 70 points, Moyes’s side sit 17th with 23, outside the relegation zone only on goal difference.