The scoreline may have been even worse had Schwarzer not pulled off a catalogue of good saves in the second half, but the Aussie stopper was frank in his assessment of the game.
"They deserved to win today because we put in what was probably one of our worst performances of the season," Schwarzer told fulhamfc.com. "We're not going to make any excuses, Everton deserved to beat us today.
"When you concede two early goals against a team as good as Everton you're always going to have a mountain to climb to get back into the game. They're a very well organised side and we were disorganised today and that's uncharacteristic for us.
"Some pretty harsh words were said in the dressing room at half time and after the game so hopefully we can pick ourselves up and make sure we perform far, far better on Tuesday night [against Liverpool]. We need to because otherwise it's going to be a very difficult week."