The Craven Cottage outfit have lost four consecutive top-flight matches, leading to speculation the Dutchman could lose his job, with Alan Curbishley - who joined as technical director in December - tipped as a potential candidate to take over.
Meulensteen's position was further scrutinised following the club's disappointing FA Cup exit to League One outfit Sheffield United on Tuesday, with Nigel Clough's side earning a last-gasp extra-time 1-0 triumph.
Next up for Fulham is a visit to Old Trafford to face champions Manchester United, and Meulensteen insists he is relishing the challenge.
"People keep saying there's pressure," he said. "I don't see it as pressure - it's a challenge, that's what it is. Life throws challenges at you and that's what you need to deal with, you need to accept the challenge and rise up to the challenge.
"We have to pick ourselves up, brush ourselves off. That's what we've done in the last couple of days and we have to make sure we're in the best possible shape to travel to Old Trafford on Sunday.
"After every poor performance you look for a response. My job is to make sure I manage that and make sure that response is going to happen. We need to grow; we need to grow as a team, we need to grow in strength.
"Sometimes bigger challenges can even result in bigger performances, and that's what we need on Sunday.
"For us it's another game against a very strong opponent where we've prepared very well. We need to get our act together and hopefully we can get something out of it."
The fixture at United sees Meulensteen face a club where he enjoyed two separate spells in former United boss Alex Ferguson's coaching staff, and he is anticipating a "special" return.
He added: "(It is) brilliant (to return); absolutely brilliant. It's just been such a special club for me, and still is. I've got a lot of friends there, and still have, and I will enjoy every moment of it."
