A group of supporters gathered outside San Siro to voice their anger and frustration at what has been a poor season for Milan, who went into the Parma clash in 11th place, 10 points off the European places and 20 behind Napoli in the third UEFA Champions League spot.
The Curva Sud, a prominent Milan fans group, issued a statement on Friday that blamed everyone involved with the club for their below-par campaign, including Galliani and striker Mario Balotelli.
And Galliani admitted the fractious relationship is hard to come to terms with, but reminded fans of Milan's recent success.
"Of course it hurts, especially as people ought to remember the journey of this squad," he told Sky Sport Italia. "I was looking at the statistic and over the last decade we've been the only Italian side regularly in Europe.
"We hope not to miss out on Europe next season, but if it does happen then it won't be the end of the world.
"I am disappointed and it's certainly not pleasing to see the fans against the team and part of the club, but I continue smiling."
A section of the fans from the Curva Sud refused to take their seats and left the stands empty as part of Sunday's protest.
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