Carvajal also appeared to throw a punch at Mandzukic, but the incident went unseen by referee Milorad Mazic.
"I saw after the game that I'm accused of biting an opposing player," Carvajal said on his Twitter account. "Let me make clear that I have not bitten anyone, or attempted to do so."
Mandzukic was in the thick of the action throughout the match and was even left bloodied after appearing to be hit in the face by Sergio Ramos' elbow.
Mandzukic's team-mate, Diego Godin, was infuriated about the incident, and said: " I was upset by Ramos' elbow, but that happens in a game and that's where it stays.
"The referee is there to decide what's a foul and if they're yellow cards or not."
However, Carvajal came to Mazic's defence, saying: "It's difficult for the referee in these games. With the tension that was generated, he was good, I congratulate him from here.
"We were the better team in the first half but we couldn't be in the second. The pitch didn't help. It can't be 0-0 at the Bernabeu. It'll be decided there."