Che Adams scored the only goal of the game just before half-time to condemn Rovers to their fifth consecutive game without victory, a result which leaves them only six points clear of the League One relegation zone.
“I would have to say I have to apologise to the fans for that, because I would not be happy if I’d watched that,” Ferguson said.
“That is not what I have come to expect from my team.
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“It’s something that needs to be sorted out quickly.
“I can’t defend that performance. It was the complete opposite of what I wanted.
“It was a surprising performance from us.
“There was no tempo, no energy, no quality, no composure.
“We had one or two maybe half things but it was a really off day.
“It was probably the worst performance since I’ve been here, on a big day like this.”
A disjointed Rovers side struggled to create chances throughout the game and failed to produced a revitalised performance in the second half, which they entered a goal down.
It meant for a rather comfortable afternoon for United who never looked like conceding their lead.
Ferguson - who watched from the Keepmoat Stadium control box due to his touchline ban - said he was left “bored” by a lack-lustre South Yorkshire derby.
He said: “Quite honestly, I was completely bored to tears by the game.
“It was one of the most boring games of football, certainly a derby, that I’ve ever seen.
“It wasn’t even like a derby, there were no tackles and atmosphere.”