The 35-year-old accepted his side were second best from start to finish in the encounter, and believes they were perhaps fortunate to escape with only a two-goal deficit heading into the return leg.
"We were up against a magnificent side and they fully deserved to win," Buffon told the club's official website.
"They had other chances to score too. We came here with confidence in our own ability. We were right not to change our game, and go for it as we did. We can have no complaints."
Meanwhile, defender Leonardo Bonucci remained bullish about his side's hopes of qualifying for the semi-finals of Europe's most prestigious club competition.
“I’m 25 years old and the game against Bayernwas the most important of my club career to date,” he said on his official website.
“I believe, I want to fight, I want to win. Right up until the end, come on Juventus Stadium, come on team Juventus. Let’s fight."
The second leg takes place at Juventus Stadium on April 10.