Three goals in the final 11 minutes at the DW Stadium on Sunday gave Wigan a stunning win which all but end Arsenal's faint title hopes and should ensure Martinez's men another season in the Premier League.
The Gunners appeared to be coasting to victory on the back of goals either side of half-time from Theo Walcott and Mikael Silvestre.
But goals from Ben Watson, Titus Bramble and a stunning winner from Charles N'Zogbia conjured an astonishing comeback which moves Wigan seven points clear of danger with three games left.
Melchiot told Sky Sports: "At half-time the gaffer said 'keep going guys, I believe in you and you can do it', and that made a difference.
"I was happy that we kept going and Charlie [N'Zogbia] got a magnificent goal."
Asked what the win would do for the Lancashire club, the Dutchman added: "It's very big. It's going to make a a lot of difference to the morale of the team and those who come and see us."
Central defender Bramble, who profited from a glaring error from Arsenal goalkeeper Lukasz Fabianski to nod the equaliser in the final minute, hailed the battling spirit of his side.
"It shows what great commitment we have," said Bramble.
Commenting on his own goal, he added: "The keeper's pushed it in the air and I got the rebound - thankfully it crossed the line."
Next up for Wigan is a game at fourth-bottom West Ham next Saturday which could secure the Latics' place at English football's top table, and Bramble warned his side cannot afford to rest easy while it is still mathematically possible to go down.
"We've got a massive game next week and we celebrate today, but we've got to prepare for next week," he said.