After England lost the Lord's Test to India, Vaughan advised Cook to take a break. But Vaughan feels that Cook has proved his leadership abilities after England took a 2-1 lead in the series.
"No question, I was wrong. Two-and-a-half-weeks ago, I said a break would've done him good. But the England and Wales Cricket Board stood by him, he was strong and said: I'm the man to carry this young team forward," said Vaughan on BBC Radio 5.
Vaughan, who had led England to Ashes glory in 2005, believed Cook should have been stood down as captain after the Lord's Test. Vaughan also suggested that Cook must be given a six-month break from cricket in order to get fresh for a busy schedule next year.
But Cook answered all his critics with with knocks of 95 and 70 not out in Southampton that England won by 266 runs.
In Southampton, Cook was given a major reprieve in his first innings when he was put down on 15 by Ravindra Jadeja. Vaughan feels the dropped catch altered the momentum in the five-Test series.
"I think that one catch is the real twist of the whole series. If Jadeja had caught Cook on 15, I really felt at that time, it would have been a disaster for the side," he said.