Ashkan Dejagah's second-half strike ended a nine-match winless run in the Premier League for the hosts, handing a much-needed boost to their survival hopes.
And Magath, who has taken charge of just four games, wants to now build on a crucial three points as the race to avoid the drop heats up.
|BATTLE AT THE BOTTOM
16. West Brom
17. Crystal Palace
"I told you before the game I am convinced we can manage it and stay in the league, and after this victory I am even more convinced," he told reporters.
"It is a good feeling to have a win at the end of the game. I think the atmosphere was tremendous the fans supported us very well.
"If you begin a new job you know you need a win, it's extraordinarily important that you have a win as the players are not confident and they need confidence."
With rivals West Brom, Sunderland and Crystal Palace also picking up points, the win was even more important for Fulham - who remain four points adrift of safety with eight games remaining.
But Magath is focussed on his own side's form, rather than looking at what those around them are doing.
"I don't care much about the other results because we have to do our work and get our results," he added. "It's not only the result today, it's the game we played, we were the better team.
"It will give us the confidence that we can avoid relegation and stay in the league."
Newcastle assistant manager John Carver, who took charge of the visitors due to Alan Pardew's stadium ban, could not hide his disappointment at the result.
"It's been a difficult day, I can't fault the lads for their effort, but we lacked quality," he told reporters. "The game hinged on a few key decisions.
"[In the build-up to Fulham's goal] Luuk De Jong gets caught from behind, we defend poorly, he [Dejagah] cuts inside and we lose the game.
"I am disappointed with the decision on Luuk but that's how it is. "I certainly counted to 10, but we have to, we have to be on our best behaviour.
"I had a conversation with Howard Webb, he explained his reasons to me and I accepted that."