"As poor as we were, I've got to give the lads credit for finishing well," said Blackwell.
"The crowd weren't happy but courage manifests itself in many ways.
"It might be going in for a header or simply just wanting to get yourself on the ball.
"And, to be fair, my boys showed courage and determination out there."
Blackwell added: "We've got far too many people coming and going through the football club at the moment so it's difficult to get any sort of cohesion."
While United breathed a sigh of relief, Derby were left wondering how they failed to beat their below-par opponents.
Rob Hulse, playing against his former club, prodded wide as early as the third minute as the visitors seized control.
United goalkeeper Mark Bunn, who picked up a knock in that exchange, later succumbed to injury as the fitness problems which have decimated Blackwell's defence continued.
Derby appeared on course for a comfortable victory after Savage drilled home a long-distance shot in the 17th minute.
Kris Commons gave Jordan Stewart, United's makeshift left-back, a torrid time down the flank while Michael Tonge, who started his career with the south Yorkshire club, drew a smart near-post save from Bunn moments before the interval.
Mark Yeates twice went close for United after the break but, when substitute Henri Camara saw a close-range attempt scrambled clear after Stephen Bywater parried Stewart's pile-driver into his path, their hopes seemed dashed.
But Williamson, the Derby-born midfielder, salvaged a point for United with an emphatic finish following Yeates' run.
"A couple of things cost us," Derby manager Nigel Clough admitted. "And one of them was failing to get that second goal.
"We were comfortable and should have been two or three up by the time that went in.
"We had plenty of opportunities to begin with and should have been out of sight.
"But, overall, I thought our performance was excellent.
"The front two led the line exceptionally well and everything else went from there.
"That set the platform."