The former midfielder says leaving out the Leicester City's star is a disgrace.
Hodgson named his final England squad for Euro 2016 on Tuesday, cutting three names from the original 26-man squad he had previously selected.
Those men proved to be Newcastle United’s Andros Townsend, Manchester City’s Fabian Delph and Leicester City star Danny Drinkwater.
Leicester City v Everton - Barclays Premier League
And Savage is one who was not impressed by the decision, labelling it as a disgrace in his reaction on Twitter.
So drinkwater left out , played so well for the champions consistently well all season , what an earth did he have to do to go #disgrace— Robbie Savage (@RobbieSavage8) May 31, 2016
I can't wait for Roy to explain decision not to take drinkwater ! #disgrace— Robbie Savage (@RobbieSavage8) May 31, 2016
He was not the only one to react, with former stars Trevor Sinclair and Ian Wright also reacting negatively to the decision.
After the season Drinkwaters had how can he not be in our final 23 when we've only pick 1 wide player? #FormNotReputation— Trevor Sinclair (@trevor8sinclair) May 31, 2016
England manager Roy Hodgson
Hodgson will now be hoping that the decision to leave Drinkwater at home does not come back to haunt him.
He has taken a risk in selecting an unfit Jack Wilshere, while there are also doubts about Liverpool duo Daniel Sturridge and Jordan Henderson.
Should any of that trio end up picking up another injury and missing the tournament, there is no doubt many will bring up the decision to drop Drinkwater in future.
England's Jack Wilshere in action with Turkey's Caner Erkin