Mark Noble had put the relegation-threatened hosts in control at the interval with a brace of penalties and had the home fans dreaming of a repeat of their Carling Cup success over the Red Devils.
But a second-half hat-trick from an inspired Wayne Rooney saw the visitors run out comfortable victors in the end, with Javier Hernandez adding a late fourth.
On what effect the nature of the defeat will have on morale, Grant told Sky Sports: "It will not damage it.
"We are a strong team and we have showed we can recover well.
"We are disappointed. It was 2-0, we played well and then they scored."
The result saw the Hammers slide back into the relegation zone, although Grant would not read too much into the loss.
"We had a big job before. We can get over this," he added.
"We came strong, we were very good in the first half and it is more disappointing."Barclays Premier League. Click here to bet.