Can you save a new rose cutting after the stem has gotten mold and wilted? There are baby roots already.?

I think the cuttings started out ok, because they have small roots ... but I must have watered them too much, because a couple of days ago the leaves and stems all started getting moldy. I took the plastic tub off, to let out the humidity from the "greenhouse", but I think it might be too late - the stems have turned black and wilted. There are still roots in the soil - is there anything I can do to still save the cuttings, or do I need to start over? They were started about 3 weeks ago.