Lewis Holtby scored Fulham's only goal in south Wales and for a short period of time with the score at 1-1, it looked like the visitors might get more than just a point.
But Cardiff captain Steven Caulker added a second goal to his first-half opener before the unfortunate Sascha Riether deflected the ball beyond Maarten Stekelenburg.
And, speaking to Sky Sports after the game, Magath admitted the defeat was a tough one to take.
He said: "We are disappointed that we lose such an important game so the relegation fight goes on.
"We were not too good today but for us it is a problem when we score too late. We played OK but one goal and our confidence goes.
"I thought we might do better when we came back but that takes our confidence away when we lose the second goal.
"Nine games [left this season] is a lot of points, but for sure we have to win our home games like Cardiff did today. It is still possible."