The Rossoneri attracted some criticism last week after pictures of their European kit for next season, bearing the Champions League logo, were prematurely published.
Vice-president Adriano Galliani said it was a simple mistake and that it would be "deranged" to read anything into it, but their rivals for third, Fiorentina, used it as motivation.
Victory for Milan against Roma last week would have secured third place in the table but a goalless draw, in a game marred by racial abuse from the crowd, allowed Fiorentina to apply pressure.
The Viola won 1-0 against relegated Palermo to move within two points of Milan. They travel to another relegated team in Pescara this weekend.
It remains a tall order for Vincenzo Montella's team to overhaul Milan but they would pip the the Rossoneri on a superior head-to-head record if they finished level on points.
Fiorentina's veteran striker Luca Toni, who scored the winner against Palermo, told the Viola Channel: "There's always hope.
"We'll have to see how Milan do, but I think it'll be tough to reach the Champions League. Still, we should be pleased with qualifying for the Europa League because it's been a great season.
"Right from the start we've been near the top of the table, we've always fought hard. I think we've played the best football in Serie A. It's a great base to build from because the team has some fantastic players."
Milan coach Massimiliano Allegri will be hoping for a favour from one of his former clubs, with Pescara one of many he represented in his playing days.
Whatever the outcome, Fiorentina are guaranteed Europa League football at least.
Udinese and Lazio are battling behind them for fifth place and the second Europa League spot. Udinese hold a two-point advantage heading into their game at Inter Milan while Lazio travel to Cagliari.
Should Lazio miss out they could still earn European football with victory over rivals Roma in the Coppa Italia final.
The other major issues in Serie A have been resolved ahead of the final round of fixtures. Champions Juventus play away at Sampdoria on Saturday with second-placed Napoli also on the road at Roma the following day, Palermo's spell in the top flight comes to an end as they host Parma, Atalanta take on Chievo, Bologna host Genoa and Torino tackle Catania.