Popov lashed in a shot off the post after 48 minutes at the Cardiff City Stadium, with Welsh woes compounded in injury time when Chris Gunter was sent off for a cynical foul on Dimitar Rangelov.
The result will not help Flynn's chances of landing the job on a permanent basis, with a theoretically trickier task ahead in Switzerland next Tuesday.
After two defeats from two games in a group that also includes England, Wales' chances of finishing even second look slender.
Yet for much of the first half Wales, in their first match since the departure of John Toshack as manager, had looked sharp and enterprising.
Playing the attacking football which Flynn had called for, they carved out clear-cut chances for Gunter and David Edwards that should have been taken.
Steve Morison also went close soon after Popov had struck but Bulgaria, apparently rejuvenated by new coach Lothar Matthaus after two opening defeats themselves, finished much the stronger.
A crowd of only 14,061 also suggested Wales still have much to do to re-engage themselves with the public.
It was the eastern Europeans who had the first serious chance when a long-range shot from Georgi Peev was deflected into Wayne Hennessey's arms.
But Wales looked energetic and Gunter should have opened the scoring after just seven minutes.
Morison let the ball run after Joe Ledley dragged it back across the area but the unmarked Gunter, looking for the far corner, fired across goal and wide.
Wales' offensive set-up did leave them open to errors in the early stages and they were almost made to pay as Bulgaria hit them on the counter-attack.
Ashley Williams, handed the captain's armband in Craig Bellamy's absence, took time to settle into his midfield role and was caught out as Popov broke clear.
Popov fed the onrushing Martin Petrov on the edge of the box but Hennessey produced a fine save from the Bolton winger.
The game began to settle down as the first half reached its midpoint.
Wales looked to Gunter and Gareth Bale on the flanks to create their chances but their balls into the box either eluded Morison or were dealt with by the defence.
David Vaughan needed to get back to deny Popov a shooting opportunity and Bulgaria had another clear-cut chance when Martin Petrov blasted over.
Bale, earning rave reviews for his Tottenham performances lately, moved into the centre towards the end of the opening period in a desire to get into the game more.
He almost got on the end of a Ledley cross and then worried the Bulgarians with a run at the heart of their defence after a Williams interception.
He was halted at the edge of the area by Pavel Vidanov - brought on for the injured Valentin Iliev moments earlier - on the edge of the box.
Wales had another brilliant chance on the stroke of half-time as Danny Collins, recalled by Flynn for his first cap in three years, picked out Edwards with a brilliant cross but Nikolay Mihaylov saved the Wolves man's goalbound header.
Bulgaria upped the tempo after the break and threatened to overrun the Welsh.
Gunter bravely blocked a Martin Petrov shot as the visitors powered forward but Wales could not hold out for long.
Popov fired Bulgaria into the lead when he collected the ball from Nikolay Bodurov in the box and beat Hennessey with aid of the woodwork.
It almost got worse for Wales as Stiliyan Petrov tested Hennessey from 40 yards with a fierce shot and Martin Petrov then broke clear only to miss the target.
Flynn was facing a stern examination but Morison almost hauled his side level when he skipped a challenge on the edge of the box and forced Mihaylov to push away a strong drive.
Hennessey was called upon again to palm away a free-kick from Blagoy Georgiev after James Collins bundled Dimitar Makriev over 25 yards out.
Flynn threw on forwards Simon Church and Hal Robson-Kanu late on.
Robson-Kanu immediately found space but picked out no-one with his cross.
The Reading man then had a chance to equalise but headed over.
Chavdar Yankov almost grabbed a second for Bulgaria in the final minute but the excellent Hennessey was equal to his low shot.
Wales were reduced to 10 men in injury time when last man Gunter checked substitute Rangelov as he looked to break from inside the centre circle.