Magath was appointed on Friday night, with Meulensteen's departure not confirmed until the Dutchman himself announced he had be relieved of his duties.
The Whites currently sit bottom of the Barclays Premier League and are four points from safety with 12 games remaining.
Crawford admits he was not expecting the change at the top but feels Magath could bring something new to the club's survival bid.
"I was very surprised," he told Press Association Sport.
"We had all read that he might have two games to save his job but you just assumed that the performances and fight they showed would have been enough.
"We have got a week's break now before a massive game against West Brom so it was the last time we could make a change.
"Magath has never managed outside the Bundesliga so getting him to come in to a team in this position is a bit of a coup and we have a £12million striker [Kostas Mitroglu] who is yet to play.
"You always need something or someone special and, in Magath, it looks as though the club have brought in an experienced fire-fighter."
Magath has won three Bundesliga titles during his managerial career but now faces a different challenge after being tasked with keeping Fulham in the top flight.
Crawford is hopeful Fulham will see a response to the appointment, something that never occurred when owner Shahid Khan decided Meulensteen was the man to replace Martin Jol in December.
"We haven't won a league game since January 1, we are out of FA Cup, bottom of the league and running out of time," he added.
"You have to look at the season we have had - usually you get a bounce off a new manager and that is something we haven't had.
"The defending has been abysmal for most of the season, you hope that someone who is a disciplinarian will come in and get things right, he won't take any prisoners and has virtually no margin for error.
"We are in the last chance saloon and everyone recognises that, it slaps a little bit of desperation but that is par for the course given the situation we are in."