Shaun Miller's last-minute goal for Sheffield United in extra time on Tuesday extended Fulham's winless streak in all competitions to five matches and eliminated the Londoners from the famous knockout competition.
The result also heaped more pressure on Meulensteen with the Dutchman having replaced his compatriot Martin Jol as Fulham's manager on December 1.
"That (Khan's support) will only last until that is gone," Meulensteen said after Fulham's loss to Sheffield United.
"So, until that time, I just keep doing my job as best as I can.
"I have no worries in that respect at all."
"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," the Dutch manager said.
"If you start falling apart within then you have an even bigger problem. That's what cannot happen."
