The Bianconeri were on the brink of taking Los Blancos to extra time in the quarter-final second-leg encounter at the Bernabeu after overturning a 3-0 aggregate deficit.
The 40-year-old goalkeeper confronted English referee Michael Oliver after the spot kick was awarded, and was subsequently sent off for his troubles.
"For over 20 years, Gianluigi Buffon has been a role model both on and off the pitch," Allegri is quoted by BBC Sport as saying.
"If on one occasion he said the things he did, in a situation as tough as Wednesday night's, that is understandable and I challenge anyone to react differently. It's always easy to judge from the outside.
"The referee had a very good game for 90 minutes, he really did. He then slightly lost his way at the end, but these things can happen.
"I don't know if it was correct or not, I don't care, but Buffon was also sent off and therefore denied the opportunity to save the Cristiano Ronaldo penalty. Gigi's reaction is to be understood."
Juve return to action on Sunday with a Serie A home game against Sampdoria.