Drinkwater turned down an England call last week, convinced he was better served working on his fitness at Chelsea, but Shearer is unimpressed.
He wrote for The Sun: “I cannot question players withdrawing from international duty claiming they are injured.
“I wonder sometimes if it were the World Cup final whether those pulls and twinges would heal quicker? But there you go.
“The one thing I do question is a player apparently refusing a call-up because he claims he has not played enough football.
“Danny Drinkwater, what were you thinking? If you have not played enough football, take the opportunity to play some!
“Going forward he is not the sort of person I would want in my squad. Given that attitude he shouldn’t be picked again.”