Goals from Mario Mandzukic and Claudio Pizarro ensured it is now 10 years since the Bianconeri have reached the semi-finals, and on that occasion they were eventually defeated by Milan in the final.
Speaking to Mediaset, the 31-year-old defender said: “We certainly played better than the first leg, but Bayern proved they are a very strong side and one stronger than us.
“We need to improve in order to reach their level and maybe by working hard we can get there.
“This was our first Champions League in many years, for some of us the first full stop. Bayern have been at this level for five or six years, but we are just dipping our toes in."
Barzagli praised the support of the home fans and hopes that the team can achieve success by regaining the Serie A title.
“We played with great fans and we thank them for supporting us. Now we have to end the season well," he added.
“It’s a shame we were unable to give them something to celebrate, but it was wonderful to receive applause even after the defeat.”
Paul Pogba has impressed in his debut Champions League campaign, but the Frenchman agreed Bayern were worthy winners over the two legs.