The Bayern defender hit the crossbar in the first half before Arjen Robben opened the scoring at the Volkswagen Arena.
But a Nicklas Bendtner equaliser in the last minute set up a penalty shootout, which last season’s DFB-Pokal winners Wolfsburg won.
“We shouldn’t be conceding then,” Boateng told Germany’s ZDF television. “I think we can be happy with our performance, we were clearly the better team with by far the better chances but if you don’t score, then it happens that you concede and we were just unlucky.
“You can’t say Wolfsburg were better than us because they actually won the game on penalties, though.
“We had chances and dominated the game from start to finish.”
But Bayern only had a Robben goal to show for that presumed domination and they could have found themselves a goal behind at the interval.
After punishing Manuel Neuer for one of his unnecessary trademark bursts out of his area, Kevin De Bruyne then lacked the composure to dispatch the ball into an open goal, although a shove in the back from Boateng did not help as the Belgian placed his shot wide.
It was a let-off for Bayern, who failed to take full advantage.
“Of course I’m disappointed and angry,” said Robben, who had lifted the Supercup twice before with Bayern.
“We would have deserved to win today, but we saw how things can transform in just a minute.”
That final minute saw De Bruyne tee up Bendtner for an equaliser which proved also that last season’s Bundesliga runners-up could push Bayern even closer for the title this season.
“We know that,” admitted Neuer. “And we’re looking forward to it too. Bring on the competition.”