Blackwell's team remain in third place, a point behind Birmingham - held 1-1 at home by Plymouth Argyle - with three games to play in the race for automatic promotion.
"If you said to me back in June when we returned for pre-season training that with three games to go we'd be in with a chance of automatic promotion, I'd have broken both your legs and your arms," said Blackwell.
The Blades manager, who hopes Matt Kilgallon can return to action next week after sustaining a knee ligament injury at Reading, added: "It was difficult.
"We saw what Forest came to do. They never really came to play, but the onus was on us to break them down, but we just couldn't get the ball to break.
"I would have been delighted with 10 out of 12 points at the start of the week, but we always get greedy don't we."
Halford forced Forest goalkeeper Paul Smith into a brilliant save with a point-blank far-post header late in the first half, but the Blades were thwarted at every twist and turn and rarely penetrated the visitors' steely defence.
Blackwell also believed Wilson deserved a straight red card for his actions, but that even without his dismissal Forest were hell-bent on stopping the Blades from playing.
He added: "There was no room for us to manouvre in their box and you've got to give them credit to be fair.
"Forest are in such a position that it would have been stupid of them to go gung-ho.
"They had to get something from the game because they're fighting for their lives.
"But I've got to look at the bigger picture and over Easter we've been excellent, so I've got no real complaints."
Forest slipped back into the bottom three despite securing four points from their last two matches, but there was no disguising assistant manager David Kelly's pride in his players' efforts.
Kelly chose to focus on his side's "super result", but admitted he could not defend Wilson's actions and confirmed the defender would be disciplined by the club.
He said: "We've no complaints with the sending off. You can't put your head there can you?
"He's absolutely gutted. But our back four were superb. They all were. It's a super result."
Forest were backed throughout by the massed ranks of their travelling fans, who made a big impression on Kelly.
He added: "Our supporters were absolutely fantastic and we're really pleased our players have put on a performance for them."