Gareth Bale and Cristiano Ronaldo cancelled out Arturo Vidal's opener, before Fernando Llorente equalised for the home side, and Conte feels that a draw with the nine-time European champions should not be considered a poor result.
"It's no disgrace to drop points against a big team like Real Madrid," Conte told reporters.
"They have great individual quality, wonderful strikers and every time they get near the goal you can feel the pressure rising.
"It won't be easy for us now. but we'll do what we can to qualify."
Conte's side are currently bottom of Group B on three points.