Ashkan Dejagah netted on 28 minutes as the Cottagers dominated the opening period in Magath's first game in charge.
But Matej Vydra slotted home an equaliser with four minutes remaining to leave Fulham rooted to the foot of the Premier League table ahead of a home derby clash with league leaders Chelsea next Saturday.
The German told Sky Sports: "I think it was a fair result because West Bromwich had more possession from the game and with the ball.
"But we had good defence and we tried sometimes to score and one time we were lucky but we needed one more.
"We had ball possession and we went forward (in the first half) and it was very good. In the second half, always playing away, you get under pressure, and we did fine until the last minutes."
Magath declared himself 'quietly satisfied' as he seeks to guide the Cottagers to safety in the coming weeks.
"You cannot change the players in a few days, it takes time but for the first game I think we did quite good," he said.
"The players are disappointed (not to win) but I said one point is better than no points so we are satisfied and look forward to the next game where we have the chance to make three points."