Milan boss Stefano Pioli praised the determination of his players to see out the win against Parma following the dismissal of Zlatan Ibrahimovic, who has denied insulting referee Fabio Maresca.
The Rossoneri were cruising in Saturday's Serie A clash thanks to first-half goals from Ante Rebic and Franck Kessie, only for Ibrahimovic - who played a part in both goals - to be sent off for dissent with an hour played.
Riccardo Gagliolo pulled a goal back for Parma six minutes later, but Milan survived a few nervy moments and added a late third at Estadio Ennio Tardini through substitute Rafael Leao.
Referee Maresca, who sent off Inter boss Antonio Conte in January, reached straight for his red card after Ibrahimovic had said something following the awarding of a free-kick to Parma.
It is the sixth time the striker has been dismissed in Serie A since his debut in the competition in 2004-05 - the joint-most for a forward alongside Francesco Totti, Goran Pandev, Domenico Berardi and Mauricio Pinilla - and Pioli has shed light on what was said.
"I was focused on the match," he told Milan TV. "Zlatan told me that he argued with the referee and that the discussion went on, but he told me that he had not offended the referee.
"The discussion took place and the referee soon reached this decision."
When asked by Sky Sport Italia if he had any idea what Ibrahimovic said, Pioli added: "He told me he said to the referee, 'You really don't care what I tell you?'"
Parma attempted 308 passes in the second half to 10-man Milan's 119 and had double the number of attempts on target to their opponents' two after the interval.
But Leao's strike at the end of a swift counter led by Diogo Dalot ensured Milan came away with a 13th away league win of the season - a club record in a single top-flight campaign.
Milan's 16 away wins this season in all competitions is the joint-most they have managed in a single campaign, meanwhile, alongside 1992-93 and 2004-05.
Pioli is pleased with the way his side reacted to Ibrahimovic's red card but cannot explain why his team have performed better on their travels this campaign.
"The positive is that my team managed to get the victory with great determination today," he said.
"Parma are tough to play, we messed things up ourselves at one stage, but the important thing was to win.
"The statistics show we do better away from home. It's strange and we are evaluating the reasons, but the games are quite similar when playing behind closed doors.".
Milan are back to within eight points of leaders Inter, but of more significance to Pioli is the seven-point gap to fifth-placed Napoli, who like each of the teams around the Rossoneri have a game in hand.
"We want to take Milan back into the Champions League. We've got strong competition from Juventus, Atalanta, Napoli, Lazio and Roma, so we have to take it one game at a time and keep going," Pioli said.
"These are all teams capable of winning eight or nine in a row, so we can take absolutely nothing for granted. Maybe we wasted too much time and energy thinking about the future or other situations.
"If you think too much about the game in a month’s time, you won't focus enough on the one that is coming up.
"We need to get back to the points average we had at the start of the season, but we can only do that if we take it one game at a time."