Shaun Miller's goal in the last minute of extra time on Tuesday extended the Cottagers' winless streak in all competitions to five matches as they crashed out in their fourth-round replay.
|7/4||Fulham are 7/4 with PaddyPower to avoid relegation from the Premier League|
"[Khan's support] will only last until that is gone," Meulensteen told the press after the game, "so, until that time, I just keep doing my job as best as I can.
"I have no worries in that respect at all."
Fulham last tasted success on January 14 with a 3-0 triumph over Norwich City in the FA Cup third round and Meulensteen implored his players not to lose faith.
"The most important thing is that we don't lose the togetherness because that's the only way we're going to get out of this mess," he declared.
"If you start falling apart within then you have an even bigger problem. That's what cannot happen."