"I'm relieved," Fergie told MUTV.
"It was so late in the game, but we got the break because we took a gamble.
"We deserved to win the match because we were the team that wanted to win.
"We decided to leave Nemanja Vidic up the pitch and leave Rio one on one with Kenwyne Jones.
"We felt that there was no threat from that side of the game. We were in complete control.
"I can understand Sunderland, in their desperation down near the bottom of the league, coming here to defend. To get a point would have been a great for them. They made it difficult.
"We had chances, but the goalkeeper made good saves in the first half. Then in the second half we had some outstanding chances, we should maybe have done better with them.
"It was hard work, and it's difficult playing against a team that is as defensive as Sunderland were. It's difficult to break them down."