The Bianconeri dominated the vast majority of the encounter after falling behind to a 14th-minute Nicolai Jorgensen goal, but sloppy finishing meant that they were not able to add to Fabio Quagliarella’s 54th minute effort and take all three points back to Turin.
Conte was left shaking his head at his side’s profligacy, venting to reporters that his players must turn opportunities into goals, regardless of the heroics of Copenhagen goalkeeper Johan Wiland.
"I do not think we have ever created so many opportunities to score in one single game before during my period as Juventus coach," he told reporters.
"During my career I have learnt that creating at least 10 glorious opportunities to score is not enough to win games if you don't put the ball in. Their goalkeeper was just amazing but we also helped him with some poor finishing."
The 44-year-old also dismissed suggestions that his team had taken the match for granted and pointed out their record in the group stage last season.
"I don't think we underestimated them because last year we drew one game in Denmark as well," he retorted.
Real Madrid’s simultaneous 6-1 thrashing of Galatasaray saw Juve lose early ground to the Spanish outfit in the battle for supremacy in Group B.