In April, Sporting Lisbon manager Ruben Amorim apologised for holding talks with West Ham, saying it was a “mistake” – and Sutton believes ongoing speculation about Moyes’ future has resulted in a downturn in results.
The Hammers have won just one of their past nine Premier League games.
“I think subconsciously players switch off,” said Sutton. “I don’t think it has been helpful the fact David Moyes has been messed around by the owners and I think it has had a knock-on effect.
“I just think they may have got this badly wrong.
“There will be West Ham fans expecting the world next season, expecting them to push on, expecting them to be more expansive and I would be surprised if it’s any better than it has been under David Moyes.
“The owners have got sucked in to the fact that there is a section of the fanbase who are entitled and they want fantasy football. That’s the long and the short of it.
“I just think it could have been handled better and he could have been shown more respect.”
Moyes’ final home game in charge will be against relegation-threatened Luton on Saturday (15:00 BST kick-off).
Hatters winger Andros Townsend believes West Ham’s owners were right to announce Moyes’ departure before the end of the season.
“There are rumours as soon as West Ham go on a bit of a bad run – ‘Oh, Moyes is going to get replaced’,” Townsend told the Monday Night Club.
“I think they [the owners] have done the right thing. They have waited until the season has petered out.”
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