The Bianconeri trainer was full of respect for the Bundesliga giants following Tuesday's encounter at the Allianz Arena
An early goal from David Alaba, followed by a Thomas Muller strike after the break, helped the Bavarians to a comfortable home win, and Conte realises his side now face a tough task to turn things around in the second leg.
"Bayern played a great game. We just came up against a great team tonight. I have to be honest and admit that we simply faced a better side," Conte said at a press conference.
"We knew it would be a difficult game but we also know that football is unpredictable and that we'll have to do something great against such a strong team in the return leg.
"Bayern have great quality but also a great physical condition and a great fighting spirit. They are up there with Barcelona and Madrid in terms of quality yet they are also very angry after losing last season's final at home on penalties. And they proved all their grit tonight.
"Bayern played with great tempo, they won almost every challenge and did not allow us to play our game. Our project started only 16 months ago, so this can be an important lesson, especially to understand what it takes to play at this level. We can just be proud to already be here at this stage."
Juve resume Serie A action on Saturday at home against Pescara.