How can opening of a door on small plane cause a drop in altitude?
In an unpressurized plane the door opening is less of an issue than in a pressurized plane but there are still some issues it presents. Its common for planes to have multiple latching mechanisms to try to prevent this from happening. In some cases they system is not perfect like this AD issued for the DA40 relating to the doors coming off in flight (due to improper closing it appears). Being able to run with out a door or open it in flight is even key for things like para-trooping and skydiving   



Depending on the orientation of the door the biggest issue I would foresee is the door shearing off and damaging part of the empennage. This could a have serious if not potentially fatal impact on the plane. 

Physically speaking the open door will create drag on the plane which may have been related to the decent you felt. It could also have been an inadvertent reaction by the pilot to the possibly loud noise.

On somewhat of a side note, most aircraft doors are oriented in such a way that the airflow will more or less push them shut (on small GA planes/non pressurized planes). Thus most doors open forwards like the ones on many pipers 

 

Or vertically up so gravity will close them (note the baggage hatch). I would assume this is intentional but it may just be coincidence as that is also how car doors open. Along the opening lines, it is standard emergency procedure in small airplanes to unlatch the door before a forced landing incase the accident mangles the door locks. 

For what its worth some planes are even flown with the hatch open most the time (pictured on the ground here but flown in the same config)



Here is a nice article written by a pilot about why it would be very hard (basically impossible) to do on a pressurized plane.