The 61-year-old resigned from his role as England manager on Tuesday after being caught up in a sting conducted by the Daily Telegraph which exposed him and his plans to make £400,000 from businessmen for advice on bending FA transfer rules.
Allardyce left Sunderland to take the Three Lions job less than 70 days ago and former star striker Shearer cannot fathom why he would throw away a position he had waited his entire coaching career to obtain.
"I'm angry, I'm sad, I'm staggered at the misjudgement from a guy who admitted this was his dream job," Newcastle United great Shearer told BBC Radio 5 Live.
"It's incredible and a catastrophic misjudgement by Sam and his advisors. I'm angry at the whole situation, I didn't think England could stoop any lower from what happened in the summer at the Euros.
"Now here we are, a laughing stock of world football. We've got a problem with money. It's greed."