The three points kept United on top of the Barclays Premier League but Ferguson admitted he feared it would not be his side's day for long periods against a plucky Reading.
Ronaldo missed a glorious chance from eight yards out, Reading goalkeeper Marcus Hahnemann made an excellent save to deny Owen Hargreaves and Kalifa Cisse cleared one from under his own bar.
But with just 13 minutes remaining United finally engineered the breakthrough as Carlos Tevez picked out Rooney in the box and the England striker directed his first-time shot past Hahnemann.
Ferguson said: "By the end we were quite happy to get through it.
"Considering the number of opportunities we had, maybe our decision-making in the final third of the field wasn't at its best.
"We kept making chances, but you do start to worry when the game goes on and you haven't scored.
"Credit to Reading, they keep going at you all the time and I think that's an important result for us."
United, who put six past Newcastle last weekend, still created enough openings to have won two matches in what was a pulsating game at the Madejski Stadium.
Ferguson added: "It was a really open match. I think it really needed a goal early on and there may have been a lot of goals in that game but we got the goal at an important time."
Coppell said: "We thought 'What have we got to lose, let's go for it' and for 70 minutes we gave as good as we got.
"If we had nicked three points it would have been history here, that is how big the opposition are. A point here would have been terrific for us.
"But you look at their incisive individuals - and by that I mean Ronaldo and Rooney.
"By and large we handled the other nine well but over the course of 90 minutes their appetite will create openings and opportunities. In the end it was one too many."