Biarritz were without a domestic win since August 24 but they finally grabbed their second league success when they edged out Racing Metro on Saturday night.
And while both scrum-half Yachvili and hooker Genevois admit there is still a long hard slog ahead of them, the pair are hopeful that they may have turned a corner a month out from their European double header with Worcester Warriors.
"We're far from being saved from relegation in the Top 14 but we had to beat Racing Metro at any price," said Yachvili.
"We did that, although we're very aware that it was very close to draw or another defeat. It was a hard-fought, tight victory but it will be very good for our moral.
"We would have liked to play better than we did and to have scored a few tries, but, with the rainy conditions, we are satisfied with the four points. We'll now work hard to push on with that win in mind.
"We've got a long way to go and we certainly won't be telling ourselves that we've arrived. But it is a relief."
Biarritz are still nine points adrift of fellow Amlin Challenge Cup sides Oyonnax, Bayonne and Bordeaux-Begles at the foot of the French table but the team spirit they showed against Racing suggests there is good reason to predict a turnaround in fortunes.
And given their record in European competition, with an Amlin Challenge Cup crown in 2012 and two Heineken Cup finals appearances to their name, there is no reason not to suggest they could soon be back on a level footing on both fronts given that Pool 1 leaders Sale Sharks still have to travel to the Parc des Sports Aguilera.
"What I will remember is our solidarity on the pitch," added Genevois.
"It was the fact that we all wore the same shirt with pride in front of a crowd who came to support us despite the bad weather.
"We wanted to be able to walk off the pitch with our heads held high. That's what we were able to do and I'm proud of that fact.
"We won that challenge at the weekend and now we can look forward."