"It was neither perfect, nor pretty, but winning here in France was the most important thing. We closed out the game well and didn't crack at the end like we have a few times this season," said Easterby.
"We probably made life difficult for ourselves in the Pool with those back-to-back defeats against Clermont, but we still might have an opportunity to get into the Amlin Challenge Cup."
The game turned into a belated birthday present for the Scarlets' Welsh international outside half Rhys Priestland. The day after he turned 27 he scored 14 points and picked up the Heineken Man of the Match award.
"To be honest, it was a poor game. At times we were our worst enemies, putting pressure on ourselves, but we worked hard. We wanted to simplify our game for this match and our pack was outstanding today," said Priestland.
"We did well. In a few games this season we have been in a situation like that and it didn't turn out well for us. But today we showed composure and managed to get that win, so that's good for us.
"We didn't get the accuracy and confidence we expected, but we showed great determination."