Martinez was under pressure after Wigan's first two Premier League games of the season in which they lost twice and also conceded 10 goals.
But following victory at Tottenham, that pressure has eased slightly.
"I rate Roberto highly and said to the fans, if you want his head, you'll get mine as well," Whelan told BBC Sport.
Whelan, who appointed Martinez on a three-year deal in June 2009, has given the 37-year-old Spaniard his unconditional support.
"Had they insisted, and even if we would have lost at Tottenham and they start crying for his head and had he asked to go, I would definitely have resigned with him," he added.