Buffon vehemently disputed referee Michael Oliver's decision to award Madrid a stoppage-time penalty that curtailed the Bianconeri's fightback from a three-goal first-leg deficit.
Cristiano Ronaldo beat Wojciech Szczesny from the resultant spot-kick after Buffon's remonstrations were met with a red card as the hosts prevailed 4-3 on aggregate.
The Italy goalkeeper later called Oliver's character into question, describing him as having a "garbage bin" for a heart, but Pirlo defended his former team-mate's emotional response in what is likely to be the 40-year-old's final Champions League game.
"His desire to win always remains," Pirlo said.
"The penalty could just as easily have not been given. If the referee is a little more shrewd he could have let it go.
"If I was on the field yesterday it would have burned me a great deal to go out in that way. When you play a game like that and then lose 10 seconds from the end it makes you crazy.
"A loss like that passes after time. The league is not over yet and the disappointment will remain, but you have to think about the league."
Pirlo was speaking at a press conference to announce a testimonial match to be held at San Siro on May 21.
The 2006 World Cup winner called time on his decorated career in November following a stint with Major League Soccer side New York City FC.