Only if it fell into the fire control group pocket, and jammed up the trigger somehow. Otherwise, it doesn't need to be in place to have a functional AR. It's only there to contain parts when you break the upper from the lower. The retainer shouldn't have come out, if the receiver extension was screwed in far enough to keep it in place - see if you can get some pics of the retainer hole in the lower, that shows the receiver extension end, in the lower receiver.
Check your hammer spring, and make sure it's installed correctly - they can be installed backwards, and cause light primer strikes.