Hodgson also had sympathy for United manager Sir Alex Ferguson, who was forced to field midfielders Michael Carrick and Darren Fletcher and rookie Ritchie de Laet in a three-man defence at Craven Cottage.
“We played well in the first half and went in 1-0 up,” the Fulham manager told Sky Sports.
“We were expecting a bit of a backlash and we were fortunate to get a very early second goal, which gave us something to hold onto.
“The shape of the team remained strong and we were then able to get a third goal.”
He added: “We were fortunate today.
“We played a United side that are suffering very badly from injury but we can’t do much more I suppose than play as well as we can play.
“But I have a lot of sympathy for Sir Alex at the moment because it is not easy when you are missing a whole back four.”
