Juventus were eliminated 4-3 on aggregate in the quarter-finals, despite Wednesday's 3-1 victory over Madrid, who benefited from a dramatic last-gasp penalty at the Santiago Bernabeu.
Buffon and Juve were poised to force extra time after remarkably erasing Madrid's 3-0 first-leg lead, until Cristiano Ronaldo broke their hearts with a spot-kick at the death.
Two-time reigning champions Madrid were awarded a penalty after Lucas Vazquez was fouled by defender Medhi Benatia, sparking a furious protest from Buffon, who was shown a red card having confronted referee Michael Oliver.
"There was too much confusion, and this is what happened," Allegri said. "Gigi had that reaction but it's understandable.
"I don't know if this will be Gigi's last Champions League game but there were three seconds left and we were close to a historical result, something he saw slip from his fingers.
"That was a human reaction and I think he should have been understood. In that moment there was a lot of confusion and the referee took out the red card. I never talk about single episodes.
"The penalty... the referee saw that and gave the penalty. There’s nothing left to say. There's a lot of regret on our part, the team played very well tonight and in Turin for 60 minutes they also played well.
"The result condemned the performance of the team but that's not what it was. That's why I was very confident on tonight’s performance."
"There's no VAR so we lost," Allegri added. "There's not much to say. This is UEFA's problem. I always said that VAR is a very important tool on objective and important decisions. But there's no VAR and we have to deal with that."
Allegri was seen in conversation with Sergio Ramos, having walked over to Madrid's bench to speak to the suspended captain following the awarding of the penalty.
"Ramos said the penalty was 'claro' [clear] and I told him: 'Not so 'claro', let's say grey'. I also told him that in the first leg at minutes 92 there was a penalty on [Juan] Cuadrado," Allegri said.
"I only told him that. But it's normal, there has to be some anger and regret because at that point Buffon was also sent off. Also, Benatia should have been sent off because he already had one yellow card. So let's just say there was general confusion overall."