The TV presenter sarcastically expressed her appreciation for a feature piece by Quentin Letts, presumably his recent attack on BBC One controller Jay Hunt.
Hunt has been accused of a conflict of interests over reports that she is a company secretary of her husband's media training firm BrightsparkTV.
Allsopp wrote on Twitter: "Lovely piece in DM in which QL is misogynistic, zenophobic & codones racism, way to go Quentin (at least he can spell, which I can't!) (sic)."
In his piece, Letts described Hunt as a "lean-lipped" and "humourless" woman with a "killer-kitten smile" who made the wrong decisions following the respective controversies relating to Carol Thatcher and Jonathan Ross.
Letts said: "She did not understand that One Show presenter Carol Thatcher, although a fool to make a private, off-air remark comparing a black tennis player to a golliwog, had done less serious and public damage to the corporation's reputation than Ross.
"She is regarded by BBC insiders as a remorseless ratings-watcher and dumber-down, one of those careerists who in the past decade has prospered at the corporation not by espousing ideals of highbrow excellence, but by trawling for viewers in easy, shallow waters."
Allsopp recently received two apologies from the Daily Mail after one article accused her of having a moustache and another wrongly claimed that she had a crush on Lily Allen.