Milan won 1-0 through Pervis Estupinan's goal, bringing the Rossonero within seven points of Serie A leaders Inter.
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Akanji said, "Milan played the game we expected, but in the first half we made a lot of mistakes and gave them several opportunities.
"The two derbies were completely different. In the first leg we dominated and they scored in their only chance, this time we made too many mistakes and weren't aggressive enough. That's why we lost.
"You're not happy when you lose a derby, but the good thing is that we still have seven more points than Milan."