Domenech's team created a hatful of chances but the Swiss just as Ireland had in October held on for a battling point at the Stade de France.
The coach believes his team must now be as canny away from home as Les Bleus' recent World Cup opponents have been in Paris, starting with the trip to Israel on Wednesday.
"The fight goes on," he said, "and all the teams are equal and now we have three matches away from home and we are going to have to treat our rivals the same way they treated us at the Stade de France.
"We wanted to win but the Swiss proved very strong and the main weakness was our failure to finish up front. If someone knows the cure for that, I would like to know it."
Newcastle defender Jean-Alain Boumsong admitted that nothing less than a victory will do in Wednesday's World Cup qualifier against Israel in Tel Aviv.
"The other teams drew so in a way the Israel match will be a must-win and our objective there will be to take all three points, and not content ourselves with only one. We trust our work and our potential to win more points and I hope we will be successful in Tel Aviv."
France were without injured striker Thierry Henry and they missed his finishing ability as they failed to find the back of the net despite a handful of clear opportunities.
This left coach Raymond Domenech hoping the Arsenal hit man would recover from his calf strain in time to line up against Israel in Wednesday's crucial encounter.
"He [Henry] was too short (of fitness) for the Switzerland clash but I hope he will play on Wednesday. For a good result I truly hope that he will be with us in Tel Aviv."
Barcelona midfielder Ludovic Giuly took heart from the result in Tel Aviv earlier in the day, adding: "Ireland and Israel drew so we have not lost hope but we are very disappointed because we just could not find the back of the net."
They had their first chance five minutes into the match when Sylvain Wiltord received a cross from captain Patrick Vieira and fired a powerful shot which slid past the left-hand post.
Switzerland responded a minute later with France goalkeeper Fabien Barthez forced to make a save following Philippe Degen's strike.
Vieira missed a golden opportunity in the 22nd minute. Wiltord started the move but his shot was stopped by Swiss goalkeeper Pascal Zuberbuhler's knee before landing at the feet of the Arsenal player who missed from a superb position.
Striker David Trezeguet was next to have a go but Zuberbuhler was ideally placed and made a clinical save.
The Juventus striker once again failed to find the back of the net in the 27th minute following a long cross from the right from Ludovic Giuly. Although at times disorganised, the French continued creating chances in vain.
Four minutes before the break Ricardo Cabanas fired a powerful shot towards the French goal but Barthez stopped it.
In the second half it was the same story. Wiltord found himself in front of Zuberbuhler but lost his one-on-one battle with the Swiss goalkeeper.
The Lyon striker failed to convert a beautiful strike in the 52nd minute when after picking up the ball on the run, he failed to create enough spin on his shot and it went past the right post.
Switzerland coach Kobi Kuhn considered it a case of mission accomplished. "That was the aim to bring a point back. It was a pretty good performance and we were playing against one of the world's top teams. I am very happy and proud of my young players who gave everything they had."
FRANCE: Barthez, Boumsong, Gallas, Givet, Sagnol, Dhorasoo (Meriem 59), Giuly, Pedretti, Vieira, Trezeguet, Wiltord (Govou 82).
SWITZERLAND: Zuberbuhler, Degen, Muller, Senderos, Cabanas, Lonfat (Huggel 29), Spycher, Vogel, Ziegler (Magnin 69), Frei, Gygax (Henchoz 90).
Ref: Massimo De Santis (Italy).