The London outfit fell to a morale-crushing defeat in Wales that keeps them four points adrift of safety at the foot of the Premier League table.
Steven Caulker scored twice for the hosts, either side of Lewis Holtby's equaliser, before Sascha Riether's own goal put the seal on a miserable day for Magath and his team.
Mitroglou made his first start since a big-money move from Olympiacos in January, but failed to impress and appeared short of match fitness.
Magath, who only took over from Rene Meulensteen once the Greece international had already been signed, said on Thursday that Mitroglou was not match fit, despite playing an hour in midweek for his national team.
However, Magath raised a few eyebrows by first selecting the 25-year-old in his starting XI and then giving him the full 90 minutes despite a disappointing showing.
"He is not used to a relegation fight," said Magath of Mitroglou.
"He came from the best club in Greece and the best club was better than the others in the league.
"He's only used to scoring and that's his strength. Here in the Premier League it's the best league in the world so he needs to get used to it.
"He's not used to it. Unfortunately he had some opportunities but at the moment he's not in the situation to score."
