Wigan's victory sends them to Wembley for one of the semi-finals in April and provides Whelan with an emotional return to the famous stadium.
Whelan was 23 when he broke his leg at Wembley playing for Blackburn Rovers in the 1960 FA Cup final against Wolverhampton Wanderers. Wolves won 3-0 and the injury ended Whelan's top-flight playing career.
Now 76, Whelan was on his feet in celebration at Goodison Park as his team eased past Everton in their first Cup quarter-final since 1987.
"It's a unique moment for the club," Martinez told ITV Sport. "It's historic, and the chairman deserves it.
"You could see in the dressing room - everyone wants to see the chairman at Wembley. What he has done for the club over the years is incredible."
Whelan, who bought Wigan in 1995 and made his fortune in the retail trade, said he had had a premonition about his team's Cup run.
"It has been an absolutely wonderful day," he told BBC Radio Five.
"I had a dream in the week that we came to Everton and beat them and then got Blackburn, who beat Millwall, in the semi-final.
"We're halfway there. I hope it comes true and I'd love to go to Wembley and play Blackburn."
Blackburn face Millwall in a sixth-round tie on Sunday, when Manchester United face Chelsea. Manchester City booked their semi-final spot by beating Barnsley 5-0 on Saturday.
Martinez, the Spaniard who took charge of Wigan in 2009, is adamant the Cup adventure will not adversely affect his side's latest bid to avoid relegation.
Aston Villa's 2-1 win at Reading in the Premier League on Saturday pushed Wigan into the bottom three while the Latics were celebrating their success at Goodison Park.
But Martinez told reporters: "If anything this Cup run has given us extra players (competing for places). This Cup success is bringing extra competition into the league campaign and that is what we need to get from this success."