The Australia international has helped guide the Cottagers to the final four of the competition in a first for the London club and ahead of Thursday’s semi-final first leg against Germany’s Hamburg, Schwarzer knows his side will again be against the odds to get a positive result.
"In every round since the group stage we have looked at our opposition and thought: 'By rights we are not supposed to be here. We are not supposed to get through to the next round,’” Schwarzer said.
"And that's worked in our favour. We've gone about our business and done our job. We've had the self-belief even though we've had a lot of doubters.”
Fulham’s real belief in the Europa League started when they defeated reigning UEFA League champions Shakhtar Donetsk in the first knockout stage and since then Schwarzer has seen his teammates grow with every challenge.
“There have been a lot of jibes and from opposition teams and players that have written us off even after the first leg, like the Shakhtar Donetsk players,” he added.
"I know (right-back Dario) Srna was very, very confident that they were going to beat us in the return leg and even after their game he has been quoted as saying on the internet that there is no way Fulham should have beaten Shakhtar and gone through. He even predicted that we'd get knocked out in the very next round.
"So it’s nice to have that in the back of your mind still. We often joke about it still as you like to prove people wrong.
"Jimmy-Floyd Hasselbaink and Bolo Zenden left Chelsea and came to Middlesbrough and all these people were told that it was a step down or that they had joined us because they couldn't play at a high level anymore.
"The similarities are here at Fulham. People said similar things about me when I first arrived. Danny Murphy as well.
"John Pantsil and Bobby Zamora were bit-part players seen as not being able to take that next step up again.
"But the things being said can create a unique environment because everybody is out to prove the critics wrong."