And, for the first half at least, it showed. James Hayter put Rovers ahead after four minutes and it could have been 4-0 by the break.
But United emerged from half-time in a different mood, keeping Rovers under steady pressure until James Harper pounced two minutes from time to end the Blades' run of seven straight defeats on the road.
After the game, Blackwell explained his side's calm disposition was helped in part by a 20-minute screening of the 1968 film Kes - and some soothing words during the break.
"I don't know the players," he said. "There are six in there who are not my players. I don't think you can steam into someone (at half time) if they are moving on in a few weeks. The psychological approach changes massively.
"Before the game, I had them watching Kes. We showed them the clip with Brian Glover giving the team talk outside the showers. Henri Camara is from Senegal and has never seen it before. He was in stitches.
"It's about taking the pressure of the players. They don't know each other. It helped lift the mood and that's what you need.
"At half-time there was no shouting.
"I just said 'you are good players. I know you don't know each other, but just go out there'. And we dominated."
It was a different story in the first period.
"We looked all over the place in the first half, to be honest," Blackwell added.
"Look at the back line: Jordan Stewart has played 11 times for us and he is not a left-back. Paul Connolly has played twice, (Marcel) Seip three times. (Steve) Simonsen has not played at all. I thought it showed."
Indeed, Rovers were up after four minutes and Hayter then missed two glorious chances - the first the result of superb goalkeeping from Simonsen, the second a fluffed header from close range - while Shelton Martis and James O'Connor both reacted too slowly to an inviting ball across goal by James Chambers.
United finally made Rovers pay with a late goal, Harper claiming an equaliser after Doncaster failed to deal with Andy Taylor's free-kick.
Sean O'Driscoll's side extended their unbeaten run to six games to remain eighth in the Coca-Cola Championship and the manager was satisfied with the result.
"We created enough chances against a very strong Sheffield United team," he said, before calling on pundits to be realistic over his side's play-off chances.
"People get carried away with things, but this is only our second season in this division," he said. "For us to get in the play-offs we need to win nine out of nine.
"Get real."
He added: "The performance was excellent today.
"They had a lot of pressure but few chances. I thought we were lucky to get away with the penalty shout (in the second half when Chambers appeared to shove Richard Cresswell). If the ref gave it I wouldn't have complained.
"We played a good team and got a point."
Source: Team Talk
Source: Team Talk