The Cottagers appeared poised to finally lift themselves off the foot of the table on the back of Ashkan Dejagah's first-half strike at The Hawthorns, but a howler from goalkeeper Marten Stekelenburg prevented just that.
Just four minutes from time, Stekelenburg fluffed a 10-yard shot from 75th-minute substitute Matej Vydra as it squirmed under his body before just crossing the line, resulting in a 1-1 draw.
Despite the Dutchman's strenuous efforts to stop it, referee Mike Dean was aided by the new goal-line technology, handing Albion their fourth consecutive home draw under new manager Pepe Mel after going behind.
"The players are disappointed because we were so close to claiming the three points," said Magath, whose side continue to prop up the table.
"But we showed a lot of fight, which is what I want from my teams, and I was very satisfied with the first half.
"In the second half we then made too many mistakes, so we go home with only one point.
"But as a team we were close together, we fought very well, we looked like a team.
"We started very well and we had chances, the same as West Brom, but the more time went on, the more we went back like in recent games.
"But I've seen enough to feel sure Fulham will stay up. I was sure before the game, and I'm sure after the game.
"We were close to a win and the next game we will win."
That is some boast from the first German to manage in the Premier League as Fulham's next match is at home to Chelsea next Saturday.
Magath, though, could not blame Stekelenburg for the equaliser, in particular as the 31-year-old otherwise pulled off a number of fine saves, with none better than in injury time to deny Chris Brunt the winner.
"He (Stekelenburg) played very well," said Magath.
"It was a shot from only a few metres and such things can happen. I don't see the keeper being at fault. I don't blame him."
Although undone by the introduction of new technology, Magath again had no qualms as he has long been an advocate.
"I wonder why everybody doesn't have such technology," added Magath.
"When everybody sees a ball is behind the line, it's terrible if the referee doesn't see it and makes the wrong decision.
"So I remain a fan. I always fought for technology in Germany."
When asked for his thoughts on the matter, Baggies manager Mel joked: "World Cup 1966!"
In the end it was a deserved point for Albion, but still leaving Mel without a victory from his six matches in charge.
With Albion a point above the relegation zone, Spaniard Mel knows wins are becoming more crucial as time passes.
"It was another spirited fightback, but before the game in my head all I was thinking about was the three points," said Mel.
"We now face three long months to ensure we don't get relegated, to work hard on the pitch for 90 minutes every game.
"And we just need to win, for the players to smile, to feel good in the head, for good work every week, and for the fans too.
"I am sure with the way we played in the second half this is the way for us to win. For me the most important player on the pitch was the Fulham goalkeeper.
"Despite the draw, this is still an important point for us."