Clough, 47, sacked by Derby at the end of September, takes over from David Weir, whose contract was terminated after four months in charge.
Weir replaced Danny Wilson in the summer but departed after one win from 10 league games left the Blades at the bottom end of League One.
"Since Neil (Warnock's) departure, some of the managers we've had, some of them occurred through circumstance," McCabe said.
"The problem these last two years is that at the business end of the season we've collapsed."
McCabe added: "Don't ask me why, but it's not the fault of the stable part of the club is it?
"Things have to be rectified and anyone who's fair-minded will say these are circumstances that the club has done everything to ensure it doesn't happen.
"It's on the field of play where success is earned or otherwise."
McCabe said he had long been an admirer of Clough.
"Maybe over 10 years or more he's been one of these people in football who you keep an eye on," McCabe said.
"Is Derby's loss Sheffield United's gain? I do believe that. Derby must have had their reasons, but I'm absolutely delighted Nigel has joined us."
Clough made steady progress during nearly four years in charge at Derby, and did not have to think long before agreeing to take on his new job.
"It's one of those jobs that's attractive because of the club's potential," Clough said. "That was the biggest factor."
Blades caretaker-boss Chris Morgan will revert back to his role in charge of the under-21s, while coaches Gary Crosby and Andy Garner have followed Clough from Derby to Bramall Lane.
"The fact they made it clear they wanted us to come here and do the job, that's a big part of it as well," Clough said.
"The stadium and infrastructure is in place, but the fan base is the biggest thing.
"You can't go anywhere without that really."
When asked if he was targeting the Premier League, he said: "No, we're two divisions off it, so we'll deal with the immediate priority of stabilising the club and getting them away from that bottom four and then we take it from there."
- Sports & Recreation