Kaka teed up Balotelli for his first, a tap in, before the Italian got his brace with a lethal free-kick in the 83rd minute - an equaliser after Livorno struck either side of half-time.
Then, in the dying stages, the former Manchester City and Inter Milan man unleashed a long-range strike that hit the underside of the crossbar before bouncing away to safety.
But the 23-year-old said he believed he would be rewarded in future for his misfortune.
"That's football. Next time it will go in," Balotelli told Sky Sport Italia.
"I have always been in good shape and never had any of the problems that were written about. I just wasn't scoring, that's all."
Balotelli conceded Milan - who are under pressure this season, dwindling in eighth spot and 22 points behind leaders Juventus - are susceptible on the counter-attack.
"We need to be more careful when our opponents go on the counter-attack, because every time they do we tend to concede," he said.
"We are playing fairly well and are scoring again at last, which was a problem before, so now we just need a little more luck."
Livorno coach Davide Nicola said his side were deserving of a point against Milan, despite Balotelli's near-miss late on.
"It is our first point against a big club," Nicola said.
"We proved that we are very organised and looking at the statistics our victory would not have been daylight robbery, even if Milan hit the bar.
"We put in a confident performance and I am happy with the way my team played. We can still improve, as this side has a lot more to give."
