David Moyes' side are yet to win in the new year, with Tuesday's Capital One Cup semi-final defeat to Sunderland coming after losses to Tottenham and Swansea City respectively, and find themselves 11 points behind Arsenal at the top of the Premier League table.
|MAN UTD LATEST
|25/1||Man Utd are 25/1 with Bet365 to win the title this season|
He told MUTV: "The fans' support is very important. The fans have been great here, especially now when we are not in the best of form and we have lost the last few games.
"We need them to support us through this time. We will get stronger and we will get better. The fans are vital in being patient with us and letting us try to get there. I am sure we will do."
Danny Welbeck has frequently been played further forward as Moyes looks to cope with an injury crisis that has also seen Robin van Persie miss out on his side's last six games, and Rooney was full of praise for his England team-mate.
"Danny's been great," he added. "He's been working really hard and he's played a few games up top now and scored some vital goals for us. He's been brilliant, especially when we've had a few injuries and he's come in and helped the team."