In 2007, the Hammers fell to a 3-0 defeat to United, and relegation looked all but guaranteed.
But inspired by Argentine ace Tevez, Alan Curbishley's Irons somehow claimed safety on the season's final day - with Neil Warnock's Blades relegated in their place.
A legal battle ensued after the Premier League found Tevez's signing to be illegal - due to third-party ownership - leading to West Ham controversially being fined £5.5million rather than deducted points, which would have seen them relegated, reports the Mirror.
United were eventually paid £18.1million in separate compensation by West Ham but Moyes feels that, ahead of their first meeting in Yorkshire since, Blades fans should move on.
“I'm sure it still rankles up there," Moyes declared. “But if I was a Sheffield United supporter, I would be looking at this new generation and this new era.
“They have got a really good up-and-coming young manager - a young British manager, I have to say.
“We can all look to the past, and everybody does. But if I was a Sheffield United supporter I would be more interested in what they are doing now."