Nigel Clough was unveiled as Sheffield United's eighth boss in six-and-a-half years on Wednesday.
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 Sky Bet 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."
Warnock left in May 2007, with Bryan Robson, Kevin Blackwell, Gary Speed, Micky Adams, Wilson and Weir having since held the manager's post.
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."