Felix Magath's side find themselves four points adrift of safety after losing their relegation six-pointer with rivals Cardiff on Saturday.
Heitinga, who joined Fulham from Everton on transfer deadline day in January, believes staying up would be like winning a trophy for the Cottagers.
"You have to believe we can still do it. I still believe in the miracle," Heitinga told the Fulham Chronicle.
"There are still 27 points to fight for, and we play some of the teams around us, but to stay in the Premier League now would be like winning the Champions League for us.
"Survival for us is the trophy. It's the same now as winning a cup or a title. The only thing that matters at the moment is Fulham. It does not matter how we survive, we have to find a way.
"The manager afterwards said to us that Fulham is a club full of history and we have to try everything to keep it in the league. But it needs to be quick, because it is already five minutes past midnight now."
Heitinga concedes Fulham's struggles are down to their defensive record, with the side currently having a goal difference of minus 36, which is the worst of any of their relegation rivals.
"It's not difficult to see what the problem is - we concede too many goals," added Heitinga. "This is a team at the moment that plays without confidence and concedes goals too easily.
"It was not good enough. We have to take a look in the mirror now because there are only nine games left.
"We need to stick together as a team, we need to have a little bit of luck. We have got the quality in the squad, but we need to show it on the pitch."