I feel sorry to hear that you were kicked out. It's totally not fair for newbs, but here are few points that you have learnt:

1. Never expect old players to wait for you.
2. You can re watch cut scenes from the journal in the inn.
3. This is old content that old player run as part of daily roulette (good exp, peotics, and gils).
4. Dungeon does not stop even if you left behind <== hence it's not fair that you got kicked out, unless there were other reasons like bad behaviours.
5. Don't worry if you left behind, the group will clear the run anyway. If you want to learn how it goes, just play from the roulette (but skip the cut scenes this time) the next day.