But Palmer, who made over 200 appearances for Sheffield Wednesday in the early 1990s and still lives in the city, is convinced Clough can turn the Blades' fortunes around if he is given enough time.
Clough, in charge for nearly five years at Derby before being sacked at the end of last month, was installed last week as successor to Weir, who was dismissed by the Blades after four months in the job.
"Nigel should never have been sacked by Derby, I think he was doing a fantastic job," Palmer said.
"I don't understand that sacking whatsoever. I think he'll do well at United because he's done it at Burton with no money at all.
"But he's got to be given time. I don't believe the sacking of Dave Weir, who was just cutting his teeth in management, was fair on him.
"I know it's a results-based industry, but they were in no danger of being relegated, so leave it for a while and give him a fair chance.
"I could understand if, two months before the end of the season David was still in relegation trouble, then I could understand them doing something.
"But it's well documented that Sheffield United stripped their wage bill and a lot of people turned the job down because of that.
"So again, it comes back down to expectations. You can't strip the wage bill and put in a rookie manager and expect him to be an instant success.
"But knowing Nigel, he's a great lad and a good manager and he's proved that. Wherever he's been he's stayed considerably longer than most other managers. He'll do a good job if given time."