Hakan Calhanoglu was "angry" that referee Daniele Orsato did not review footage of the incident that saw Ante Rebic dismissed as Milan were eliminated from the Coppa Italia by Juventus.
Friday's semi-final second leg at the Allianz Stadium was the first professional match in Italy in three months due to the coronavirus-enforced suspension.
The game finished 0-0, with Juve's away goal from the 1-1 draw in the first leg at San Siro in February enough to send them through to a final against Inter or Napoli on Wednesday.
The Bianconeri should have taken the lead in the 16th minute when Orsato awarded a penalty for a handball by Andrea Conti following a trip to the pitchside monitor.
Cristiano Ronaldo's spot-kick came back off the upright and 17 seconds later Rebic was shown a straight red card for a dangerous lunge on Danilo, who he caught in the chest with a high foot.
Calhanoglu was frustrated Orsato did not follow the same process for that incident.
"We are quite angry, because if the referee checked VAR for Ronaldo's penalty he had to check it for Rebic's red card," Calhangolu told Rai Sport.
"We're cross, but we played well and the only thing missing was a goal.
"Over the two legs it's difficult to say who deserved to go through. I think if we had [suspended trio] Zlatan [Ibrahimovic], Samu [Castillejo] and Theo [Hernandez] here we'd have been stronger.
"It's natural that games with Juve are tough, but they were very even."
Milan's only remaining avenue for European qualification is through Serie A.
Just four points separates Stefano Pioli's side in seventh with Cagliari in 12th and the Rossoneri boss was gutted by their elimination.
"It's a pity as this was our objective and we didn't manage it, so now we must qualify for Europe via Serie A," he said.
"It was a very narrow difference over the two legs, it's just that by conceding at home we were then forced to score in the second leg.
"We held out exceptionally in defence, especially the centre-backs, and that shows us we can be solid, because we need these skills going forward for the rest of the season.
"It's disappointing. We really wanted to play the final. What we need now is to be more consistent, because so far this season we haven't taken home the results we deserved, as our finishing hasn't been up to scratch and we didn't convert enough of our chances."Published 13 Jun 2020, 04:00 IST