A brace from Roma striker Pablo Osvaldo saw the Azzurri pick up a point in Sofia in Group B.
"A point is valuable, especially as we always have a few problems at the start of the season," said Prandelli.
"It's also a shame, as we had the chance to go 3-1 up three times and would have had fewer issues towards the end, taking some of the wind out of Bulgaria's sails.
"We played below our tempo and were not precise in our passing, but above all we allowed Bulgaria to run at us and were chasing their tempo."
Italy's next game in the group is against Malta in Modena on Tuesday.