First-half goals from Leighton Baines and Kevin Mirallas kept Roberto Martinez's side in the hunt for Champions League football, while condemning the Reds to their 11th Premier League defeat of the season.
Former Everton player Rooney felt that his side played well in the early stages, but their lack of an attacking threat and lapses in concentration at the back cost them dearly.
"We're obviously disappointed with the result," he told MUTV. "I thought that in the first half we moved the ball well, but we just didn't penetrate enough.
"We moved the ball quite well and they were struggling to get near us at times, but we just had to try to break them down. They sat quite deep, so we might have needed more width or more runners in behind to create space but it was a difficult game.
"Everyone knows that it's a difficult place to come and Everton made it difficult for us by putting bodies behind the ball, but we conceded two really sloppy goals which we need to cut out because we're making it hard for ourselves to get back into games."
United are currently seventh in the Premier League table.