Allardyce has taken issue with Shearer claiming current Magpies manager Eddie Howe has "lost some fight" in him during a difficult campaign.
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"He's totally out of order," Allardyce said on the No Tippy Tappy Football podcast.
"He's just doing it for his own popularity again with Newcastle fans; he should know better than to do that.
"Mind you, he's a pundit, and he needs to keep his reputation up, and you need to criticise if you're a pundit, don't you?
"Eddie probably knows (that the end of the road) is coming.
"We all have our life span. Sir Bobby Robson was one of the best, but even he got stick. We all get stick if we don't do well no matter who we are and we all get moved on."