Forget about the old mechanism of qualification to the Europa League. There have been made some major changes to the Coppa Italia-related rules for this season and this will affect AC Milan's chances to earn a spot in the European League
Starting this year, only the actual winner of the Coppa Italia will be automatically qualified for the group stage of the Europa League. In case this team has already qualified thanks to its final position in Serie A, the other finalist will not take its place as it has in past years. Instead, priority will be given to Serie A standings.
This would mean that the top three teams will qualify for the Champions League as usual, while the next three, instead of only two, will take Italy's Europa League spots, leaving the rights of the Coppa Italia winner to the fourth-best team in the league.
This scenario seems to be quite realistic regardless of tonight's outcome between Inter Milan and Juventus, because both of them are expected to finish among the Serie A top five. That means advancing to the final of the Coppa Italia won't be enough for the Rossoneri this year, unlike in years past. Their chances to qualify for a European competition will not be bettered as they would have been under the previous rule, so despite yesterday's huge achievement, Milan will have to focus on the Serie A for the last ten games of the season to book a berth in Europe.