The former striker believes his old club acted unprofessionally in the whole affair.
McClaren was sacked on Friday afternoon with the club moving quickly to secure Rafa Benitez as his replacement.
It brings an end to a disastrous spell at St James' Park for the former Derby County boss in which they have failed to kick on following serious investment in the summer.
There had been speculation about his future all season and Shearer says the club should have sacked him sooner, especially after last week’s loss to Bournemouth.
“I think it’s a good coup to attract someone of Rafa’s stature,” he told BBC Sport.
“I think the inevitable happened to Steve McClaren. Once they decided to sack him, they should have done it last Saturday night or Sunday morning.
“To leave him, drag it out and embarrass him for that period of time was very unprofessional.”
The pressure is now firmly on Benitez’s shoulders to prove he has the ability to save the Magpies from relegation this season.
There is no denying he has vast experience as a coach, but he has spent most of his career fighting at the top of the league and in the European places, not in a relegation battle.
That lack of experience could be crucial, and with only ten games left he will certainly have to hit the ground running in the North East.