Alan Shearer claimed it was “bizarre” that Kane – a real threat in the air – was asked to take them.
Ray Wilkins added that the decision “baffles the life out of me”.
Sam Allardyce managed his first England game on Sunday and put Rooney on corner-kick duty.
Kane, meanwhile, revealed he and the new Three Lions boss has been exchanging banter on the subject.
Asked if he expected to take corners again, Kane said: “Probably not.
“We had a bit of a laugh and a joke with the manager about it, but it’s something that happened.