Juve missed out on the trophy, losing 4-3 on penalties after 120 minutes of action had produced a 1-1 draw.
The Italy goalkeeper saved a penalty from Gianluca Lapadula in the shoot-out, but saw his 600th Juve appearance end in disappointment after misses from Mario Mandzukic and Paulo Dybala.
Buffon felt Juve should have had the game won long before that drama, though, pointing to their dominance of the early stages, when Giorgio Chiellini put them ahead, with Gianluigi Donnarumma making a string of other key saves.
“We should have realised that we could have killed off the game in those blistering opening 25 minutes,” captain Buffon told the club’s TV station.
“Milan were really struggling then and we could have won it. But, after those 25 minutes of domination, it was a very even contest. They showed determination and played well.
“It is a shame, especially as we led both in normal time and on penalties.
Buffon, referring to the 2014 Supercoppa defeat against Napoli which was also played in Qatar, added: “The regret is that like two years ago we were in front during the shoot-out and didn’t finish it,
“It’s disappointing because we could have stopped the game from dragging on for such a long time.
“We had chances, so did they, and it ended like this.”
Buffon attempted to keep a sense of perspective as Juve’s year – one that saw them win Serie A and the Coppa Italia – came to an end on a negative note.
He continued: “I don’t think fatigue because of the matches we have played was an issue – our squad is accustomed to this sort of strain.
“We have had a good year. There were lots of good things. Our 2016 doesn’t end the way we wanted it to, but that’s part and parcel of the game.”
Giacomo Bonaventura scored Milan’s goal as they won their seventh Supercoppa – tying Juve’s record.