Juventus were beaten 2-1 at the Bernabeu but their cause was certainly not helped by two harsh refereeing decisions.
Real were awarded a penalty, which Ronaldo converted, for a seemingly innocuous shirt tug by Chiellini in the 29th minute and worse was to come for the defender.
Chiellini was running alongside Cristiano Ronaldo and put an arm across him but the Portuguese star went to the ground holding his face and the referee showed the red card.
Turin-based newspaper Tuttosport declared this morning that 'the referee and Ronaldo were decisive' and blamed 'a dubious penalty and an absurd sending off' for the Bianconeri's defeat.
Juventus' players responded in a similar fashion after the final whistle of a game they had dominated for long spells.
"The red card was ridiculous and it stopped us being able to get an equaliser," midfielder Pogba lamented.
"To come back with 10 men is difficult. We're sad at our position in the group but it's not over. There are still three games to turn things around and we want to win them."
Spanish marksman Fernando Llorente had scored to level the game at 1-1 and also felt his side were hard done by.
"We played well and had lots of chances to score," he told Sky Sport Italia. "But the referee changed the game when he sent off Chiellini. It was an unjust red card because he didn't commit a serious foul on Ronaldo."
Juventus are third in Group B and trail Galatasaray by two points while Real Madrid are now seven points clear of them.