The English Premier League champions lost to Tottenham Hotspur on New Year's Day and that result was followed by an FA Cup exit at Swansea before more cup misery came in the shape of a 2-1 reverse in the first leg of their League Cup semi-final with Sunderland.
United now lie 11 points behind Premier League leaders Arsenal heading into this weekend's fixtures, with their hopes of finishing in the top four and so qualifying for next season's UEFA Champions League under severe threat.
United's supporters have also watched their team lose four times already in the Premier League at Old Trafford this season, the defeats adding to the pressure manager David Moyes already faced in succeeding the retired Alex Ferguson.
But Rooney, battling to be fit to face Swansea after missing the last two games with an abductor problem, urged fans to remain loyal to both the team and Moyes.
"The fans' support is very important," Rooney said. "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," the England striker added.
"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."
RVP nearing a return
It is not clear if Robin van Persie will be fit to return to action against the Swans.
The Netherlands forward has been out for a month with a thigh strain and media reports in Britain suggested he has returned to training but Moyes is expected to provide an update on his fitness on Friday.
Jonny Evans was taken off in the midweek defeat by Sunderland with a back problem and it is not clear if he will be able to feature while Rio Ferdinand, Nani and Marouane Fellaini are all sidelined.
Swansea will be without wingers Pablo Hernandez and Roland Lamah who have hamstring and abductor problems respectively, while goalkeeper Michael Vorm is not ready to return yet from a knee operation.
And after sending United out of the FA Cup last weekend with their first-ever win at Old Trafford, Swansea boss Michael Laudrup said there was no reason they couldn't do it again.
"In many recent games we played with a lot of confidence but just needed the win and sometimes that win comes when you least expect it," Laudrup explained.
"Maybe others didn't expect us to win at Old Trafford but we believed and we maybe had a bit of luck scoring in the last minute," the Denmark football great added.
"Our aim is to do it again and we know it's possible because we have confidence, but on the other hand we know it is more difficult than last time because of the circumstances and with United losing at Sunderland.
"We will expect them to come out and want to go at us and want to win because they have to win this game.
"So we have to be ready for a very tough game because I don't think the United players will like what they hear about the negative record at the moment."