I'm with CAcycling: Just go ride the damn bike. You joined a group ride and couldn't keep up. I've probably done that a hundred times. The group isn't under any obligation to slow down for you, or wait for you, or be sure you're OK (I'll relax that last statement if you suddenly clutch your chest and fall off the bike, but not if you're upright and riding). I would have tagged along behind, or taken a cutoff, or gone off on my own exploring, or turned around and gone back to the start. I might have wished I were in better shape so I could have ridden with the pack, but I can't think of a circumstance where I would have been offended or blamed the group or worried for one second about it.