He might prefer three points against West Ham on Sunday, but Danny Murphy's goal was decisive as Fulham registered their first Europa League group win.
With Claudio Ranieri's Roma beating CSKA Sofia 2-0 in the other game, Fulham find themselves top of Group E.
Manager Roy Hodgson said: 'I was pleased with the way we dug in, stuck at our task and came out in the second half and started to get some passing movement going.
'It was a tight game and it could have gone either way. All the time you're only one goal in the lead, the last 10 minutes are going to be tough.
'This was an important victory. We've still got maybe five or six important players to come back and they'll be coming back rested. So it's nice to win and to do it having given a chance for players with slight injuries to recover.'
Just as in the first group match against Sofia, when an inexperienced team ground out a 1-1 draw, Hodgson picked a Fulham side just about good enough to win. But only just.
The Fulham boss has extensive knowledge of Swiss football, having managed the national side, Neuchatel Xamax and Grasshopper Zurich in the 1990s, and he shuffled his pack to good effect last night. With Damien Duff, Dickson Etuhu, Simon Davies, David Stockdale and Brede Hangeland injured - although Hangeland's ankle problem is not expected to keep him out at the weekend - Hodgson paired Chris Baird and 19-year-old Chris Smalling in the centre of defence.
Hodgson had no goalkeeper on the bench as UEFA turned down his bid to register former Basle player Pascal Zuberbuhler.
The Fulham boss said UEFA's decision 'denigrated' the competition and added: 'We literally don't have three goalkeepers in the club.
'It's not a decision they (UEFA) can expect me to understand.' Basle's 2-0 win against Roma had promised much, but the visitors had limited chances.
Benjamin Huggel should have put them ahead after 24 minutes from Marcos Gelabart's chipped delivery and Marco Streller had a gilt-edged chance to equalise with seven minutes to go. Murphy's deft free-kick after 35 minutes represented their best first-half effort.
The same player found the net in the 57th minute after Andrew Johnson cut the ball back from the byeline for the captain to score right-footed.
Hodgson also felt Fulham should have had a penalty when Johnson went down just before the break, but referee Michael Weiner waved away his appeal. The additional assistant referee - six officials were in action at Craven Cottage for the first time - wisely chose not to argue with the German referee, who is a part-time policeman.