The Europe-chasing Everton can pave the way for bitter rivals Liverpool to win an elusive Premier League title by taking points away from City, who are in the box seat to win their second premiership in three years.
Anything but a victory for Martinez's Everton would rule them out of UEFA Champions League contention, although an Arsenal win over West Bromwich Albion on Sunday would end Everton's hopes regardless.
Four points separates Arsenal (fourth) from Everton, with the latter not yet assured of a UEFA Europa League spot, with Tottenham lurking three points back in sixth.
And Martinez said their own predicament is exactly what the club is worried about, not Liverpool's, as they look to bounce back from a poor 2-0 loss to Southampton at their last start.
"Liverpool can rest assured Goodison will be the toughest place for City to travel this season, that is for sure. This game is vital for us – we need the points," Martinez said.
"I am not insulted by the suggestion we will lie down, no. I just think it's more football rivalry, a bit of banter, which I can understand.
"I would be more hurt or insulted if we had nothing to play for. But we have too much to fight for. Fans have been saying, 'If we win, great. If we lose, it's not a problem'.
"But I don't think anyone at Everton would want their team to lose. We need one point to guarantee European qualification and want six points because the Champions League is still open. For us, it means everything to win this game."
Martinez understands the passion the fans have for the game, and the lack of love they have for their neighbours - recalling a timely anecdote involving this season's UEFA Champions League finalists Real Madrid and Atletico Madrid.
"We played Atletico Madrid, who needed Real Madrid to win away at Tenerife for Atletico to get into Europe automatically. Madrid needed a victory to win the league," Martinez said, referring to the end of the 1992-93 La Liga season.
"But Madrid were losing and the Atletico crowd was going crazy, even though that meant they were not guaranteed Europe. I couldn't figure that one out.
"The line they used after the game was, 'We would rather lose one eye as long as the neighbours lose two.'"
However, Martinez pointed out that when he took his Wigan side to Stoke at the end of the 2010-11 campaign needing a win and the latter with 'nothing to play for', he was taken aback.
"We had to win that last game, and I thought they (Stoke) might be half-hearted because they had nothing to play for," he said.
"But they were going mad. Tony Pulis wanted to finish in the top 10. I'd never seen anything like it, but that is the British game and I love it. We should never lose that."
