The struggling Blades disposed of Weir's services on Friday evening having won just one of their 10 league fixtures this term, with the former Scotland and Everton defender having only taken over in June in what was his first managerial job.
Motherwell boss McCall, who finished his established playing career at Bramall Lane, hopes the South Yorkshire club can be restored back among England's elite.
He said: "It was supposed to be a three-year plan there with Dave because they didn't have the finances at the beginning of the season that a lot of the other clubs have got.
"But unfortunately we all know in management that it is a results-driven business, even though it is an unfortunately short time that Dave had the chance to implement his own thoughts and ideas to see the fruition of it.
"It is sad and I feel for him.
"It is a club that I have a special bond with because I had five brilliant years there. I just hope the next appointment is a successful one and a lucky one."