Zlatan Ibrahimovic apologised for the red card that cost Milan dearly in their Coppa Italia exit to rivals Inter, coach Stefano Pioli has revealed.

Ibrahimovic, who had scored his 499th club career goal to give Milan the lead, was sent off for a second bookable offence as he felled Aleksandar Kolarov just before the hour-mark.

Romelu Lukaku equalised from the penalty spot soon after and Christian Eriksen's stoppage-time free-kick settled a controversial Derby della Madonnina encounter.

Ibrahimovic had earned his first yellow card in a confrontation with former Manchester United team-mate Lukaku.

The two forwards went head-to-head in a heated exchange that saw Ibrahimovic aim offensive language in the direction of his opponent.

It was a major misstep and Milan paid the price for Ibrahimovic's ill-discipline, but the 39-year-old was apologetic, according to his coach.

"Ibrahimovic apologised. He knows he created a problem for the team," Pioli said. "He apologised because he is a great man and champion.

"It's clear that the game was more difficult one man down in a game so balanced. It has been crucial. It wasn't supposed to happen but it happened unfortunately.

"We felt the fatigue in the last 30 minutes and we didn't achieve a positive result.

"We wanted it and we prepared for it. Now we go back to the league and to Bologna."

Milan remain top of Serie A, two points ahead of second-placed Inter, as they aim to end a 10-year wait for the Scudetto.