In regards to the OP's Brayflox run, sounds like there wasn't much you could have done and you have to not take those negatives to heart.

On a general level, I want to offer a perspective that it is important to identify every opportunity for improvement and become better, even if the wipe wasn't your fault. As a healer, you have more ability than anyone else to make the difference in a run, especially when things aren't going well. You have more power to fix other people's mistakes and salvage runs than anyone else. That is actually one of the reasons I like healing. When there is a wipe, I often think back on what more I could have done and learn from it.

Story time: Snowcloak back when it was in EX roulette. Party was a Pally, Dragoon, Ninja, and me as a Scholar. Not a good composition for ginormous pulls, but our tank didn't realize this and proceeded to pull the entire first section up to half the wolves. By the time he stopped pulling more stuff, he was already over half dead and had over a dozen mobs on him.

I stepped up with the most epic healing job I have ever done. I kept him up for over a minute. I used my cooldowns masterfully, spacing them out perfectly without a single point of wasted overhealing. Eventually, however, I ran out of gas. Tank was out of cooldowns too. I spammed Adlo desperately but I quickly realized it was not quite enough. The last 25% of the tank's health probably took a good 10 seconds or so. Some of the mobs were close to dying. Aetherflow had around 15 seconds left for cooldown. Tank went down and everyone else shortly after.

The wipe was clearly the tank's fault for doing too big of a pull, yet I have wondered if I could have saved the run. I don't believe I could have done any better for most of the fight, but in the end, I actually had 3 cooldown abilities left: Fey Covenant, Virus, and Swiftcast. FC would not have helped with all the physical damage. Virus probably was not worth the second or so it would take out of Adlo spam to cast because there were so many enemies. But Swiftcast? Had I swiftcasted an Adlo or Physick, I could have kept the tank up a little longer. Maybe long enough for a mob or two to die, shifting the tank's net HP flow out of negative. With Aetherflow coming back soon after, the battle would have tipped in our favor and we would have won.

A few months later, I found myself in a similar situation of being out of cooldowns on a big pull and needing a little more to keep the tank up. I popped Swiftcast+Adlo and we won that one.