"Lubo (Penev) made a lot of mistakes," Bulgarian Football Union (BFU) executive committee member Ventsislav Stefanov told local media. "I want to thank him for his work and to tell him goodbye."
Bulgaria were beaten 1-0 by Croatia on Friday and then suffered a 2-1 loss in Norway three days later that left them fourth in Group H.
Croatia and Italy are top on nine points from three matches, followed by Norway on six. Bulgaria have three points after their 2-1 win at Azerbaijan in their opening fixture last month.
Former international Emil Kostadinov, another BFU executive committee member and ex-team mate of Penev's at CSKA Sofia, was also disappointed with the Oslo defeat.
"We have problems in all areas," the former Bayern Munich and Porto winger Kostadinov said. "The arrogance of coaches and players played a nasty trick on them."
Even BFU president Borislav Mihaylov, a known admirer of Penev, hinted that the former striker could lose his job, saying the executive committee would discuss the issue at its next meeting.
Penev, however, remained upbeat about his team's chances of finishing third in the group and reaching the finals for the first time since 2004.
"We're only three points behind third place, which is our aim," Penev said. "I'm optimistic and sure that things will end well."
Local media criticised Penev after the poor displays as well as his "inappropriate selections" with fans taking to web forums and social media to express their frustration.
Sports newspaper Merdian Match also slammed Penev, saying he should resign immediately after being "the architect of Bulgaria's worst performance in recent years".
Penev was appointed Bulgaria coach in November 2011, replacing German Lothar Matthaeus, whose contract was not renewed following a dismal Euro 2012 qualifying campaign.
(Reporting by Angel Krasimirov; Editing by John O'Brien)
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