Fulham are four points adrift of safety with 10 games remaining, six coming against teams in the bottom half of the table, including Saturday's at 19th-placed Cardiff.
"I'm convinced that we will avoid relegation because we've developed in the last 14 days," said Magath, who was appointed last month.
"The team is growing together and that is what makes me sure that we can avoid relegation."
Three points at Cardiff would provide a welcome boost, Magath admits, but the west London club are not too worried about their predicament at present.
Magath added: "These three points are very important for us, not only to step up from the last place, we need a win for ourselves, for our confidence.
"I get the feeling here that everybody knows that and everybody sleeps well with the knowledge there are games ahead of us we can win.
"We are in London, we are not in Cardiff or Sunderland where the whole city is interested in playing Premier League.
"The atmosphere here is really relaxed for the situation we are in; it's not typical for a team fighting against relegation.
"We have to be aware that we are not only dreaming, but everybody has to put in a shift and push the team and push the players to give their best."
Magath knows that relaxed approach cannot filter through to his players, but he is undecided if Kostas Mitroglou will feature in Wales, despite the £12million striker playing an hour for Greece in midweek.
"He is not match fit," Magath said.
"He played only 60 minutes and has hamstring problems. We have to wait, he comes back today, our doctor has to see him and maybe if he is fit he will play.
"We need a player in our situation who is prepared for 90 minutes relegation fight."
Mitroglou's situation has confused Fulham fans, but Magath insists it is unfair to heap hopes on a player who will take time to adapt to English football.
The manager said: "The Premier League is the best league in the world, so it cannot be compared with the Greek League. Every player who comes from the Greek League needs a few weeks to adapt.
"You cannot expect such a lot from a player who is new in the Premier League. You have to give him time to adapt.
"We know that and we make a contract with Mitroglu not for the game against Liverpool or Manchester United, but for the last games.
"If he's not fit now, he will be fit next week."
As a result Mitroglou was not risked for last week's loss to Chelsea.
Magath added: "Why should I spoil him in a game like Chelsea? Chelsea is the best defending team in the league and so we would get not many chances against Chelsea.
"He's new and he needs confidence, too. To get used is not good for him and not good for us."
Lewis Holtby, on loan from Tottenham, also did not start.
The forward, who played under Magath at Schalke, has been told he is not the right sort of player for a relegation fight, but may be given a chance against Cardiff, where he may have more space to play to his strengths.
Magath added: "We are not in a normal situation. Now is not the time to play very well, now is the time to fight.
"Lewis Holtby is not a fighter. He is very smart, he is a very skilful offensive player who has very good passes.
"A game against Chelsea, the best team in the league, we had not much space to create chances and therefore he was out for that game. Saturday is another game. We will see."
Winger Damien Duff, who is out of contract this summer, may have played his last game for Fulham as a knee injury is likely to rule him out for the remainder of the campaign.
Magath said: "We have to expect that he will not play this season any more."
Midfielder Scott Parker is out of the Cardiff match with a knee injury.
"It's not so bad, but for Saturday he can't play," Magath added.
Defender Fernando Amorebieta is still sidelined, while William Kvist is likely to miss out with hamstring problems, despite playing 90 minutes for Denmark at Wembley on Wednesday night.