The 3-1 defeat to relegation rivals Cardiff City on Saturday saw Felix Magath's side cut adrift at the bottom of the table, with safety now four points away.
Fulham have not won in the league since New Year's Day and have only taken two points from a possible 27, and Heitinga reckons maintaining their top-flight status would be a major achievement.
"You have to believe we can still do it," the Netherlands international said. "I still believe in the miracle.
"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 (after the Cardiff defeat) 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."
The 30-year-old defender admitted poor defensive displays were the cause of their downfall and vowed to do everything to turn their fortunes around.
"It's not difficult to see what the problem is – we concede too many goals," he added. "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."
