The Cottagers are propping up the Premier League table and are five points from safety with just a dozen matches remaining.
The west London club removed the Dutchman from his post on Friday, less than 11 weeks after being given the job.
Since then they have won just three times in the league, while collecting just a single point from the last six games.
And Meulensteen claims the club have "hit the panic button on emotion and fear."
Talking to Sky Sports News, Meulensteen said: "Chief executive Alistair Mackintosh rang me to break the news that they had brought in a new manager in Felix Magath."
The out-going boss also admitted he had no idea that he was in danger of losing his job and says he had held a fruitful chat with chairman Shahid Khan earlier in the week.
He added: "We had an extensive meeting on Monday afternoon as our meetings have been very good throughout.
"Good open dialogue and good discussions as I explained why Fulham were in this position.
"But it wasn't an easy starting point taking over from Martin Jol (who was dismissed in early December."
As for his time in charge at the Cottage, he went on: "We've had some really good performances but not results and it knocks confidence.
"We knew we had to put some new life into the team with some new players, more energy and quality, and we addressed that in the transfer window and got some new players in.
"But I've not been given enough time to finish the process. Everyone could see the difference in the performances against Manchester United and Liverpool - and what direction I was taking."
Regarding the club's decision to fire him, he stressed: "It doesn't make any sense. You'd have thought it would have happened three weeks earlier to give the new man the opportunity to bring his own players in.
"All the players coming in have come in on my recommendation. I felt the owners were on edge but I had a long-term plan in place and we were moving in the right direction.
"But it's a shame it's turned out like this. But I enjoyed my time at Fulham and the fans were good."
Former Fulham player and Sky Sports pundit Tony Gale said he felt "nothing but shock".
Gale, who was at Craven Cottage from 1977 to 1984, went on: "Felix has a history of being a hardliner. But he's only been given 12 games."
He also told Sky Sports News Radio: "They've found out that Rene is a good coach but probably not the management material that they thought he was.
"I thought it might have been the case that maybe Alan Curbishley took over but it's a bit of a gamble with Felix Magath. He's got that track record in the Bundesliga, but nothing in England.
"I can only assume that they've had a look at training and within the dressing room, with experienced people like Curbishley there helping out, they've thought that Meulensteen isn't the man for the job.
"Fulham have to do something because they need a bit of geeing-up to get out of where they are.
"If they do go down, which is looking likely, what experience has Felix Magath got in the Championship? I must admit it's a strange decision but I hope it's the right one because it's a wonderful club."