The teams came out to a wall of noise from both sets of fans as the sun baked down on the lush new surface at the Brandywell.
The hosts settled well and should have edged in front on 12 minutes after a scintillating run down the left-hand side by Kevin dos Santos.
The wide man left three defenders in his wake before whipping a great ball across the face off goal, which the sliding Adam O'Reilly just failed to turn home.
Ioannis Pittas, who bagged a double in the first leg, went close to breaking the deadlock on the night as he showed quick feet to get a shot away in the box, but Brian Maher was down quick to block with his legs.
Leandro Godoy had a goal-bound header blocked by Patrick McClean on 35 minutes, before the striker fluffed his lines from eight yards out on 41 minutes after he found space from a corner.
Right on the half-time whistle the hosts were inches away from levelling the tie on aggregate after more great work by dos Santos.
The tricky winger beat his marker before playing in Michael Duffy, who raced into the box before rattling the post with a shot from a tight angle.
The momentum continued after the break as Derry City got their just rewards when Ellis Chapman headed in a knock back from Brandon Fleming as the hosts looked rampant.
But the lengthy delay changed the momentum of the game again as Pittas nipped in between Patrick McClean and Brian Maher to restore the visitors' lead with 14 minutes to go.
Despite ramping up the pressure in the closing stages it was the Bulgarians who added to their lead thanks to Cotter's own goal with Derry City now dropping into the Conference League, where they will play NK Rijeka of Croatia in the second qualifying round.