Cardiff took the lead through Steven Caulker late in the first half of Saturday's game, but Fulham equalised when on-loan Tottenham Hotspur midfielder Lewis Holtby finished from close range.
However, Caulker, who was an unused substitute in England's friendly against Denmark on Wednesday, restored his side's lead eight minutes later, before Sascha Riether's own goal put the game beyond Magath's men.
"Our chances are worse than before (to stay up)," said the former Bayern Munich manager. "We have to win our home games, that is the most important thing. The next game is a home game against Newcastle and we need three points.
"The second goal breaks us. If you come back into the game, especially in an away game, and you score, then you are very eager to get more and the second goal came too early. After that we are not able to come back." Defeat leaves Fulham four points below Cardiff, who currently occupy 18th place in the league table, and three points behind second-bottom Sunderland who have three games in hand.
Magath also defended his surprise decision to give 19-year-old Cauley Woodrow his first-team debut, two months after the forward's last appearance during a loan spell at fourth-tier Southend United. "I see no gamble in it because he is a very talented player and I was satisfied with him," the German said. "He did a lot of work for the team and I was very satisfied."
Cardiff manager Ole Gunnar Solskjaer praised his side's reaction to Fulham's 59th-minute equaliser. "We couldn't even consider losing this one. Both teams knew they would be adrift if they lost," said the former Manchester United striker. "The response after they scored was the biggest thing for me. There is fight in this team. They are fighting and desperate to stay up. It is an experience, playing in the Premier League."
Although Cardiff are level on points with fourth-bottom West Bromwich Albion, the Midlands club have a game in hand, but Solskjaer believes that his team will survive as long as they take a minimum of 12 points from their nine remaining games.
"We've looked at the games - nine games to go and if we get another four wins, I think that'll be it," he said. "We've had a bad run, but are still in with a shout. One more win in the next couple of games will be important. I believe in these lads. When you do work with them every day, you do believe."