Milan, who are unbeaten in six consecutive derbies and have won four of those meetings, edged past Inter thanks to Christian Pulisic's close-range finish early in the second half.

The American reacted quickest after Yann Sommer pushed an Alexis Saelemaekers effort straight into his path, allowing him to guide the ball into an unguarded net.

Inter created chances of their own, but Milan's defensive discipline held firm. Strahinja Pavlovic's foul on Marcus Thuram handed Inter a golden opportunity from the penalty spot, yet Mike Maignan produced the defining moment of the match. The French goalkeeper guessed correctly to stop Hakan Calhanoglu's penalty, delivering another decisive intervention in a derby that demanded intensity from start to finish.

Speaking to DAZN, Allegri admitted the performance was far from flawless but insisted his players handled the game's pressure with maturity.

"It was a great win in a very entertaining match," Allegri said. "We struggled a bit in the first 15 minutes, but then the team grew and we created four or five situations where we should have finished better. We needed to use Saelemaekers more because Dimarco was pushed very high and we could have hurt them."

Allegri also highlighted the importance of Milan's defensive focus, praising his players for managing Inter's direct play. "They are deadly when you press them and they link well with their forwards and midfielders. We defended well, even on set pieces."

The Milan head coach admitted that their failure to win so-called simpler fixtures had frustrated him but stressed that the table reflects their true level at this stage.

"The head-to-heads give great joy, but the league is also won by beating smaller teams," he said. "We need to improve our attacking pressure. This week we finally trained together and that will help us physically. Claudio Filippi prepares the goalkeepers for penalties, he is outstanding at that job."

Allegri added that the win reinforced his belief in the squad's ability to perform when the stakes are high. "Tonight's result is especially important psychologically. We could have dropped five points behind Inter, which is not huge, but staying in the top four matters."

Pulisic and Rafael Leao both started, a combination that Allegri said he has full confidence in. "It worked well, and it already worked in Australia. Nkunku is important too – we need everyone. Training together this week helped increase the tempo."

Milan remain firmly in the race near the top of Serie A two points behind leaders Roma after 12 matches, and Allegri's latest derby triumph only strengthened belief that his side are equipped for a serious challenge.