The Danish minnows are playing in the Champions League for the first time in their history but a Mikkel Beckmann free kick saw them take a surprise lead against the Italian giants.
Juventus equalised with 10 minutes remaining to earn a point but Buffon was angry that they were unable to secure the victory.
Buffon told reporters: "I am angry for the result and for the way that we conceded the goal.
"We conceded a very avoidable free kick on the edge of the box and that was frankly the only way that they could possibly score against us. The free kick was perfect and I couldn't do anything about it.
"The first half was balanced, but after the break, there was only one team on the field. Never more than tonight was the result down to a single incident."
The draw in Denmark meant that Juventus remained in third place in Group E behind Shakhtar Donetsk and Chelsea.