Trailing to an Adam Szalai strike shortly before the interval, the visitors created several goal-scoring opportunities before Valeri Bojinov netted a deserved equaliser with three minutes remaining.
"The players were not good, they were not even excellent, they were perfect," said Penev, who succeeded German Lothar Matthaus after Bulgaria's dismal Euro 2012 qualifying campaign.
"We were the better team on the field and I feel sorry that we didn't score another goal to grab victory.
"We outplayed them, we kept possession for long periods and the important thing was that we created scoring chances and not that we missed them.
"We'll begin to score more goals, I have no doubt," added Penev, who recently said one of his main aims was to instill a "total football" ethic in the Bulgarian team.
The 45-year-old, who led Litex Lovech to the Bulgarian title last season, next faces the tricky task of piloting Bulgaria through a 2014 World Cup qualifying group that contains Italy, Denmark, Czech Republic, Armenia and Malta.
"We played very well and showed a new, positive face," goalkeeper Nikolay Mihaylov said. "There's a huge difference between Penev and the previous coach.
"We finally played as a team. Penev and his staff brought a lot of optimism, many things have changed since their arrival."
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