The Reds came from behind to sink the division's bottom club thanks to two second-half strikes by Adnan Januzaj and Rooney was pleased with the way the champions battled in adversity.
After missing the Champions League tie with Shakhtar Donetsk, the England international was keen to help his side go into the two-week break on a positive note.
"I think that’s what we needed, to get the three points and to show a bit of character as a team," the striker told reporters at the Stadium of Light.
"A win like this can turn things around. I think us, as players, know we haven't been good enough. A new manager has come in and we haven't been good enough for him.
"Obviously the manager is under a bit of pressure but we know, as a team, it's us who have let him down. We have to pull together for the manager and show the sort of fight we have done here and we'll be fine. This will be a transition season because it’s a new manager with different styles and we have to adapt to them. More importantly, we need to do better for him than we have been."
David Moyes mentioned Januzaj in the same breath as Rooney when discussing youngsters he has handed debuts and the Belgium-born prodigy can certainly be proud of his full league