Manchester United parted ways with Mourinho last week, choosing to axe the 55-year-old and place Ole Gunnar Solskjaer in charge until the end of the campaign.
The Red Devils have made a winning start under Solskjaer, who oversaw their thumping 5-1 Premier League win over Cardiff on Saturday.
Manchester United could strengthen their squad when the transfer window reopens in January, with Solskjaer reportedly set for a £50million windfall.
Mourinho craved additions in January but, ultimately, the board did not trust him to turn things around.
And Warnock believes United were not sold on Jose Mourinho spending because of how he had failed to coax the best from Paul Pogba, Romelu Lukaku, Victor Lindelof, Eric Bailly and Alexis Sanchez.
“I wouldn’t say the board sold him short,” Warnock told Express Sport.
“They bought Paul Pogba for £90million.
“Now if you’re getting backed in the transfer market with Pogba for £90m and [Romelu Lukaku] for £75m, then no complaints.
“You’ve got Victor Lindelof and Eric Bailly too, two players he wanted.
“Then you’ve got players on big money, like Alexis Sanchez.
“So he was backed but you have to look at Manchester City have done and what Liverpool have done.
“They don’t buy bad players at this moment in time. They are very shrewd.
“At the moment, United don’t seem to be doing that.
“You can understand the board saying ‘we’ve already bought you two defenders so you can’t have two more.’
“He wanted Sanchez, but he’s not been playing, he’s not been good enough.
“So you can understand the club not backing him. But they did give him a new contract in January.
“So they had to either back him or not.”
United have been linked with January moves for Douglas Costa and Kalidou Koulibaly.
But whether they secure any reinforcements in the New Year remains to be seen.