The German, a Bundlesliga-winning boss with both Bayern Munich and Wolfsburg, replaced the sacked Rene Meulensteen last week in what appeared a final throw of the dice by Fulham owner Shahid Khan in a bid to beat the drop.
Fulham are presently bottom of the table, four points adrift of safety, with just 12 games left this season to climb out of the bottom three.
But speaking ahead of his first game in charge of the Cottagers, away to West Bromwich Albion on Saturday, Magath told Sky Sports: "In the next months we will have a lot of work to avoid relegation but in the first days here the work we've achieved has been very good.
"I'm sure we will avoid relegation with this team as the players are willing to avoid relegation. We have a good atmosphere at the club when we all work together. We are able to avoid relegation and that's now the most important thing.
"Now we have to concentrate on the next 12 games, especially on the game on Saturday against West Brom."
Magath, out of work since leaving Wolfsburg in October 2012, did not have much sympathy for Meulensteen or former Fulham assistant manager Ray Wilkins and technical director Alan Curbishley, who've now all left Craven Cottage.
"I was sacked a few times also, I know the situation and I'm sorry for each coach," Magath said. "But we have here a situation where the management waited a long time.
"I think if you want to change something you have to do it now. It was late to change the team and change the atmosphere to have a chance to stay in the league.
"It doesn't look like it worked well enough so I don't care about the reason for the manager before (why he was sacked). I don't know what he had done, I don't care.
"I take over my duties and look forward to doing the best I can."