Home captain Stilian Petrov became the second player from his country to reach 100 caps, following Bulgarian Football Union president Borislav Mihaylov (102), but was unable to inspire his side to their first home victory over the Swiss.
"This is not a good result for either team," said visiting coach Ottmar Hitzfeld. "Bulgaria outplayed us in the first 30 minutes and I was impressed with the way their players controlled the game.
"But then we created some opportunities and unfortunately we couldn't score. Now we need a little miracle to reach the finals."
Switzerland also had their chances, with skipper Alexander Frei's bullet header being parried by keeper Nikolay Mihaylov on the half-hour.
"We played well but couldn't achieve the right result," said Bulgaria coach Lothar Matthaus. "I always remain optimistic until the very end but we have to accept we no longer hold our fate in our hands.
"It was a game between Bulgaria and Switzerland and not between me and Ottmar Hitzfeld," added Matthaus referring to his fellow German. "But it was a pleasure for me to face him."
