Don't worry about it. Not every dungeon is a smooth ride and sadly you had not very nice party members. Usually, at least for me, are the healers the ones that are oversensitive and abandon the duty at the first wipe saying that the party is noob and don't know how to play. Just ignore this event and keep in mind the other 3 years of duty were you had fun.

Also, in this particular case, I think the tank is the one that have most of the blame (im a main tank btw). As a tank you control the flow of the dungeon, even if the healer wants to go 300 km/s, if the tank doesn't want it, the healer is just gonna get killed while the tank is behind. I always (and almost all the tanks I know) wait for every party member to be ready before advance, specially if someone is watching a cutscene but it applies too if someone was left behind like this case.