Fernando Llorente scored a second-half equaliser to earn the Italian champions a valuable point in their attempts to qualify for the last 16, with Conte full of praise for the performance his side put in.
"I'd rate our performance very highly. The team did very well and the first half was perfect in every respect, organisation, quality and intensity," he told Sky Sport Italia.
"In the second half we suffered a little at keeping that tempo with such a packed fixture list. When the intensity drops against Real Madrid, you inevitably risk paying the price, especially when Cristiano Ronaldo and Gareth Bale are running at you on the counter.
"Iker Casillas was Man of the Match in my view and saved Real Madrid on several occasions."
Juventus are currently bottom of their group with three points from their first four games.