The Tottenham Hotspur man was perhaps at fault for Iceland's first goal on Monday.
The Tottenham Hotspur right-back has courted criticism for failing to track the run of Ragnar Sigurdsson whose goal led to the Three Lions being dumped out of Euro 2016 earlier this week, with manager Roy Hodgson quitting his post as a result of the shock 2-1 defeat.
Walker, in his defence, was one of England's better players in a competition which saw a number of them - including his Tottenham team-mates Harry Kane and Dele Alli - fail to bring their club form to France.
But the defender has won no allowances from Carragher, who said the 26-year-old 'completely switched' off in an error which he can see no defence for at this level.
"Watch the replays again [of the first goal] and you will see Harry Kane, our centre forward, running back from the halfway line to take a designated position to deal with what was coming," Carragher wrote in The Mail.
"But, inexplicably, Kyle Walker completely switches off and lets his man go. Could you imagine an Italian defender doing the same?"
Tottenham had five representatives in the England side in total, along with Eric Dier and Danny Rose.
Their labours in France might have shaken their confidence a little and Spurs boss Mauricio Pochettino may need to pick up the pieces when they return for pre-season training next month as another Premier League season draws nearer.