Substitute Ashkan Dejagah's goal gave the Cottagers their first win in the Premier League since New Year's Day, with Magath's side now four points off safety.
The German boss has revealed his pride at the result and remains hopeful that his side can avoid relegation.
"We are very proud and we are very happy. I think that this is now the point where it turns," he told Sky Sports.
"We need confidence and I know it takes time.
"We hoped we could get a win and of course, that was the one thing that we need."
The former Bayern Munich manager insists he was confident they would grind out a result, despite a drab first half at Craven Cottage.
Magath made five changes heading into the game and he believes the decision to drop key players, such as goalkeeper Maarten Stekelenburg, ultimately paid off.
"I was hopeful at half-time, and I'm lucky and glad we have managed it," he said.
"I had to make some changes for today and you never know how it works, but fortunately it was good for us.
"It now gives the players confidence in the next games."