United made a bright start and Wayne Rooney scored on his return from injury in the ninth minute, finishing from close range after good work from Anderson and Javier Hernández.
The Hammers offered little threat and failed to test United goalkeeper Anders Lindegaard at Old Trafford, although the visitors were denied a spot-kick when the ball appeared to strike Rafael’s hand.
It was a dysfunctional United performance against a dogged Hammers side, typified by Rooney’s late penalty miss – his tenth for United – after Jordan Spence was penalised for handball in the visitors’ area.
However, despite the striker’s rash attempt, the Red Devils held on to set up a home tie against Fulham in the fourth round.
“I think so [West Ham were on the wrong end of key decision],” Allardyce told ITV.
“There’s no doubt about the difference between Rafael’s handball and Spence’s handball. Jordan Spence plays for West Ham away against United, and Rafael plays for the home side at Old Trafford.
“It’s got to be that simple when you see it. The referee was in the perfect position – it was arm to ball, he [Rafael] pushes it away with his left arm – but no penalty.
“The other end, Spence arm comes up and the ball hits his hand. If you’re going to give one then you’ve got to give both. Simple as that.”
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