"The way their goalkeeper was performing you start to think it might not happen. He made five fantastic saves in the match," Fergie told Sky Sports after the 1-0 win.
"I thought we played well but, as we know, Bolton are a very difficult team to play against and in a local derby you are always happy to win the match.
"When you are attacking teams like Bolton you are always worried about the counter attack.
"There were one or two moments in the second half when we had to deal with one or two difficult crosses and you have to keep your concentration and focus. I think we do that very well.
"Of course we left it very, very late."
The win at Bolton saw United leapfrog Liverpool to claim top place in the Premier League able - the first time they have occupied pole-position this season.
"Being top is not decisive at this stage, but it is always nice because it is the best place to be," Fergie added.
"We have been playing catch-up in terms of fixtures for a while now. We still have another game in hand against Fulham on February 14th.
"Only after that will we have a good idea of where we stand between Liverpool, Chelsea and ourselves."