Former boss Rene Meulensteen signed the forward from Olympiacos for approximately €15 million, after he scored 17 goals in all competitions for the Greek giants during the first half of the campaign.
There were high hopes that the 26-year-old could make a big impact in Fulham's battle to stay in the Premier League, but his career in west London has yet to take off.
Mitroglou has been limited to two appearances for the London club due to a lack of fitness and is yet to find the net but Magath, who replaced Meulensteen in February, has defended his predecessor's decision to sign the Greece international.
"He is here and has his own programme but he is not training with us," the German told The Guardian.
"We hope [he will train] next week. You never know – you can't say it was a mistake [to sign him] because it is not easy to build up a team in the winter time.
"During the season if you want to improve your team with new players, you don't have much choice. There won't be many players you can get.
"You have to see the long term. If you take a player like Mitroglou you are not thinking only for weeks.
"So it is not a mistake – he is a very good striker who has not only scored in his national league but also in the Champions League."
Fulham remain in dire need of points to preserve their Premier League status ahead of Saturday's clash with fellow strugglers Norwich City.
Magath claims just one goal from Mitroglou would be enough to make his signing worthwhile - provided it keeps them in the top flight.
"Maybe he will help us by scoring in the last game," the German added. "That would be good enough if we stayed in the league."