Mazzarri's men would have gone third in Serie A on goal difference with victory at the Stadio Renato Dall'Ara but were unable to add to Jonathan's 51st-minute equaliser after Panagiotis Kone had put the home side in front.
The Milan side struck the crossbar on two occasions and created plenty of opportunities, but Mazzarri fears they will drop more points this season unless they are more clinical in front of goal.
"We created even more chances than usual. It looked like the goal was cursed and in these situations you can even lose," he told Sky Sport Italia.
"We made a series of naive errors (for) Bologna's goal and it made the game an uphill struggle. We missed the seemingly impossible, but that is football and if you don't take your chances then you don't win.
"If we want to stay at the top level, then we can't keep throwing points away like this."
Mazzarri also confirmed that Yuto Nagatomo was forced out of the match with a calf injury and a further update is expected on the Japan international's condition on Monday.
Inter remain unbeaten on the road this season and they return to San Siro next Sunday to face struggling Sampdoria.
