The 34-year-old Juventus stopper had made half a dozen crucial stops to help his side to a 2-0 half-time lead following a brace from Mario Balotelli.
But Buffon was left incensed that his side were hanging on at the final whistle after spurning at least four counter-attacking opportunities to put the game to bed when still leading by two goals.
Instead a Mesut Ozil penalty in injury time ensured Italy had a nervy final few minutes.
"I was annoyed at the final whistle because I don't celebrate second place and I was angry with us because we could have avoided the difficult final five minutes," he fumed.
"When you can score seven goals against Germany, you have to score seven because if they come back to 2-2 they'll beat you 10-2 in extra-time.
"We need to be more mature and to know that even if football is a game, when you reach the European Championship final, it's no longer a game."
Buffon was particularly unimpressed with the attitude shown by certain younger members of the squad.
"I also evaluate things based on certain behaviour and there's still things to improve.
"There are youngsters who have to learn this because otherwise the old guard like me gets angry.
"We played a great game, we could have won by more. We did very well today and things went well."
Italy coach Cesare Prandelli backed his captain's stance.
"Gigi is a World Cup winner and when you have three or four chances to finish a game you should do it," he said.
"It only takes a penalty or a free-kick to put this game back into question, so obviously he's annoyed. This is the mentality of a champion."
For Andrea Pirlo, who was named man-of-the-match by former Manchester United and Denmark great Peter Schmeichel, there is no reason to celebrate yet.
"I've always given my best and now we deserved to reach the final and we have to make the most of this moment," he said.
"But I don't laugh a lot because we haven't done anything yet.
"There's no use going to Rome and not seeing the Pope. We want to go home with this Cup.
"Sunday we'll have the same spirit of fighting and running that we showed against England (in the quarter-final)."
For Giorgio Chiellini, who unlike Buffon and Pirlo was not part of the 2006 World Cup winning squad, this victory was worth celebrating.
"We're living a dream and millions of Italians are with us," he said.
"We'll enjoy this win a little more and then we'll start thinking about Sunday because we want to keep dreaming."