Ibrahimovic had given the Rossoneri the lead, but after his dismissal for a second yellow card, Romelu Lukaku converted a penalty and Christian Eriksen completed the turnaround with a stoppage-time free kick.
“It's disappointing that we went out, because we cared about this competition," Pioli told RAI Sport.
“The performance shows we are a strong team who can hold out well, but going a man down made it much more difficult."
The coach was asked if the row between Romelu Lukaku and Ibrahimovic before half-time influenced the rest of the game.
“The situation was an influence, as the first yellow card then led to the second. They are two grown-ups, they said something to each other, I don't know what. It happens, we have to look forward.
“What didn't work was that down to 10 men, it was much more complicated, and we were naïve with the foul to give away the penalty.
“However, I leave this defeat feeling much more positive and confident about our future than I was after the Atalanta game.
“It was a very balanced match, the only difference was having a man down. If it was 11 against 11, it was open to any result and we were 1-0 up."