The German - a Bundesliga winner with Bayern Munich and Wolfsburg - replaced Rene Meulensteen last week with the remit of lifting Fulham out of the bottom three with only 12 league games remaining.
Ahead of Saturday's game against West Brom, Fulham are four points shy of 17th place and safety, but Magath is optimistic they can secure their top-flight future through hard work.
He told Sky Sports News: "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 had been out of work since leaving Wolfsburg for the second time in October 2012 and expressed limited sympathy for Meulensteen and his assistant manager Ray Wilkins and first-team technical director Alan Curbishley, who have all left Craven Cottage.
"I was sacked a few times also, I know the situation and I'm sorry for each coach," he added. "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."