The Royals took the lead twice but ultimately succumbed to a Robin van Persie match-winning strike after just 34 minutes at the Madejski Stadium.
Victory put United three points clear of rivals City ahead of next weekend's Manchester derby at the Ethiad Stadium.
And although England star Rooney was not happy with the way the side defended, he was relieved after collecting the points.
He told The Sun: "It was crazy out there - it was not good defending at set-pieces and it could have cost us.
"We had to make sure we were better in the second half and we did that.
"It probably doesn't do the coaches or the fans any good watching that.
"But we always believed in ourselves and when we went behind twice we came back.
"Having seen the earlier results, it was important to come away from here with three points regardless of the performance.
"When you look back at it, it was like a basketball match, which maybe delighted the neutral fan."