Following the blow, Wilkins has claimed that Benitez's decision to rest Cole for Chelsea's 2-1 defeat to Southampton on Saturday made the full-back more prone to injury.
"He never played on Saturday at Southampton, he plays 15 minutes against United and Danny Welbeck takes him on a run and he pulls his hamstring," Wilkins told talkSPORT.
"I honestly feel he has to play all the time, Ashley. He is one of these machines. You have to keep it well oiled and it will fly. Had he played on Saturday, he wouldn't have done that yesterday."
Chelsea will face Manchester City in the semi-finals of the FA Cup.