"You start wondering [whether you'll score], but in the last fifteen minutes we always knew we'd get three or four more chances," he told MUTV.
"With the talent we've got, you keep thinking 'we'll score the next one'. Rooney and Ronaldo, who have been doing so well for us lately, managed to put the ball in the back of the net.
"Getting a clean sheet is important, because if we do that then we know we're going to have the chance to win the game. That was one of the main things for us today, keeping a clean sheet.
"We had a lot of opportunities in the first half, but we didn't put them away. In the second half it followed a similar pattern, but we managed to get two goals later in the game.
"We were lucky that we got that today, but I think we created enough to chances [to deserve it]."
Reading certainly made United work for the victory, and it took a moment of class to undo Steve Coppell's side.
"That was probably the hardest game we've had all season," Rio added. Reading worked us very hard. They pushed us all over the pitch and we had to battle for our three points today.
"For Wayne's goal, the ball in from Carlos was exquisite. He picked out Wazza, and he stretched his leg out and managed to guide it past the keeper. I think he took the keeper by surprise with how early he hit it, it was a great goal."
"All three of us could have dropped points," said Rio, "but we've all won. We're just pleased with our result. We've not conceded a goal and we've won the game."