Following those two defeats, some bookmakers made Martinez, who joined the club as manager at the start of last season, the favourite to become the first Premier League manager to be sacked this term.
But 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," added Whelan, who is also Wigan's owner, on BBC Radio 5 Live.
In 1995, Whelan bought Wigan - then in the old third division - with the club winning promotion to the Premier League 10 years later.
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