The west London club are rooted to the bottom of the table, four points adrift of safety with 10 games left to play this season.
But six of those matches are against teams in the bottom half of the table, beginning with Cardiff on Saturday which Magath insists is a must-win game.
"I'm convinced that we will avoid relegation because we've developed in the last 14 days," he said. "The team is growing together and that is what makes me sure that we can avoid relegation.
"These three points (against Cardiff) 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 confirmed club-record signing Kostas Mitroglou is struggling to be fit for the weekend trip to Wales despite playing for one hour in Greece's 2-0 friendly defeat to South Korea 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."
Magath says he is keen not to put too much pressure on Mitroglu, insisting any player moving to the Premier League needs time to step up.
"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," he added.
"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."