Bakary Sako's first-half strike leaves the Cottagers still searching for the first league win of the season and second from bottom in the fledgling Championship table.
Magath insists he is the man to turn things around, saying: "The message is sorry for the defeat but I can only ask for patience.
"We have a young team and I know it might be a tough beginning to the season but I am sure we are going the right way."
However the patience of chairman Shahid Khan, making a rare visit to Craven Cottage, may be starting to wear thin after his team of rookies - six starters were aged 21 or under - tasted defeat once again.
Magath added: "We met not only today but a few days ago, we talked about the situation and he knows the beginning of the season might be a difficult period if you changed a lot and have a young team.
"We need a win, sure. If we get three points it will build up our confidence. It's a long season so I don't worry about the situation now."
Wanderers, by contrast, are a settled, well-organised side who ran away with League One last season and look capable of making light work of the Championship.
They tore into Fulham from the off and took a deserved lead after 15 minutes when Scott Golbourne's low corner was dummied by Dave Edwards and allowed to run all the way to Sako, who drilled it into the bottom corner to open his account for the season.
Ross McCormack, Fulham's £11million striker, endured another frustrating night with his one sight of goal arriving just before the hour mark - and his drive from the edge of the area was always rising as it cleared the crossbar.
Instead it was Wolves who always looked like adding to their tally, with Matt Doherty and Danny Batth both missing the target with close-range headers before Sako blew their best chance in stoppage time, hitting the post with a penalty after Cameron Burgess had tripped Nouha Dicko.
Indeed Wanderers currently look far more likely to challenge for a return to the Barclays Premier League.
Wolves boss Kenny Jackett said: "I thought we played very well. There is a good hunger and desire to get a result in the squad.
"I'm pleased with how we've started, we've won two out of three and played well in the one we lost, so we feel it's looking promising going forward this season.
"We are all looking for one of those three promotion places, and with the size and history of this club our aspirations are to get Wolves back in the Premier League."