A free-kick from Owen Hargreaves, a Park Ji-sung header and a Simon Davies own goal sealed the win for United to keep them right behind Arsene Wenger's men.
"I didn't think it was a great game at Fulham. It was a very windy day and a lively pitch but I think we did the job very professionally.
"We switched the team around and gave Rooney and Ronaldo a break. So it is a good day for us.
"You've got to have faith in your squad. You've got to trust your players. That's why we've brought them here. Look at the ones we've left out. Carrick, Giggs and Vidic would get a game for any team. They are all top players.
"Fulham played well but were not a threat in the box. The one thing with them was they always kept pushing and pressing the ball. They made a couple of chances, you know."
But Fulham boss Roy Hodgson was still optimistic about his team's chances of dodging relegation - despite admitting they still probably need five wins from their last 10 matches having won only three of the first 28.
He said: "I don't think five wins is an impossible task. It's a big task but not impossible.
"Manchester United have a wealth of talent. Three-nil sounds as though we've been totally outplayed but I don't think that was the case. We were not outclassed.
"For me it is simply back to work but not back to the drawing board because a lot of our football shows a lot of promise.
"We must try to keep people's heads up and attack these last 10 games. I knew it would be very tough when I came here. I'd done my research but I've been very pleased with the response I've had from the players, the way they have approached the task.
"I'm sad but not downhearted."
