If the needle is withdrawn from the airbrush, the trigger assembly can simply drop out, as the only thing that keeps it in place is the needle, which passes through the shaft of the trigger. This is not a problem.
If you didn't disassemble the air valve, it's unlikely that the return spring has gone missing. This would only happen if you removed the air valve assembly and, in turn, disassembled that.
It may simply be that you have screwed the needle tensioning collar in too far and it's causing the trigger to bind. When you pull back on the trigger, is it very tight? Is the action smooth? Try backing off the adjusting collar a little and see if the trigger frees up.