The Cottagers are currently three points adrift at the bottom of the table and four points from safety, with just nine games remaining to turn around their flagging fortunes.
However, Hangeland believes Fulham can take confidence from the way they escaped six years ago after a string of victories in the closing weeks.
And the Norwegian centre-back has called on his team-mates to keep battling hard to get back on track, starting with Saturday's home clash against Newcastle United.
"The only thing that will pull us out of this situation is hard work and belief that we can do it," said Hangeland in the Daily Mirror.
"We have to stop feeling sorry for ourselves and the situation we are in and pull in the same direction.
"That year when we survived, we slowly turned the ship around in the quality of training, and the belief that we could do it. We had a system and bunch of players who followed it. That is obviously an example that we need to try and replicate.
"We are under a lot of pressure - everyone can read the league table. But we have to try and pick ourselves up as soon as possible. There is one way and that is to fight together as a group."