A dour game was won by Charlie Lee's second-half strike, while at the other end goalkeeper Joe Lewis made a fine late save to deny County midfielder Kevin McDonald.
Ferguson said: "It was a character performance. It was a real battle.
"Joe has not had much to do but he's made an outstanding save. I'm delighted, it's a big win. It's a tough place to come because they've got a good home record.
"We had to dig in at the end. You have to at places like this.
"I know they've faltered in the last week or so but maybe the Cup games have hindered them. It's an awful pitch but we kept going. It took a great goal to win it."
Source: PA
Source: PA