The idea of "failing forward" is important to Fate. Put simply, failing forward means that each failure - a missed roll or a botched action, losing a fight, taking serious damage, and so forth - shouldn't stop the story, but should change its direction. For example, when the PCs try to stop a supervillain from robbing a high-tech lab, they might succeed in preventing the theft. But if they fail, and the villain escapes, a new direction for the plot appears: stopping him from using the components he stole to build a dangerous invention which threatens the city! Rather than saying "you failed", the GM has raised the stakes on the overall story.
When a fight is not going well for the PCs - particularly when fighting an unfamiliar villain for the first time - it's appropriate to the genre to allow PCs to concede, rather than taking serious damage that could linger with them through the story arc. The villain will get away, but the PCs will earn valuable Fate points that can be used to improve their odds next time.
The GM can introduce genre stunts (see "New and Optional Rules") that promote this sort of play.