The Cottagers broke their transfer record to land the Greece international from Olympiakos in January, with a £12million fee required to bring him to England.
Fulham made their move in the hope that that a proven goalscorer would aid their bid to secure Premier League survival.
Mitroglou has, however, been restricted to just one start and one substitute appearance for his new employers.
Magath has taken a tough stance when it comes to the 26-year-old's fitness - or lack of - but the German is confident that a big-money acquisition will prove his worth - possibly before the end of a campaign which continues to see Fulham battling to beat the drop.
He said in the Daily Telegraph: "He is here and has his own programme but he is not training with us. We hope next week.
"You never know - you can't say it is a mistake 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 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.
"Maybe he will help us by scoring in the last game. That would be good enough if we stayed in the league."