Conte said that the defeat was down to a couple of errors on the night, but that he saw many improvements from when they faced Bayern Munich in last season's tournament.
"I liked how the lads played tonight," UEFA.com quotes Conte as saying. "We proved we can play at this level if we really want to. Tonight we only lost due to a couple of small details, a couple of things that did not go our way.
"We played at the same level as Madrid and we could even have won. Now everything is certainly more difficult but we proved we can be competitive against any opponent.
"Last year we were outclassed by Bayern while this season we played a great game against a team who are more or less at the same level as the European champions. So I don't think we are in crisis as many said on the eve of the game – quite the opposite actually."
Juventus have two points from their opening three Group B games.