As Bluebirds goalkeeper David Marshall bounced the ball, Samuel Eto'o nicked it, leading to Hazard netting in the 4-1 win.
The laws of the game stipulate that when a goalkeeper bounces a ball it is within his control and the strike should not have stood.
But, far from siding with his fellow stopper Marshall in a goalkeeping union, Cech accepted referee Anthony Taylor's assessment of the situation, an interpretation which infuriated Cardiff.
"It's always a difficult question, when you lose control or not lose control," Cech said.
"What I know is that if you throw the ball to kick it out, nobody can touch you because it counts as one motion.
"In terms of bouncing it's not one motion, so it's totally up to the referee to decide whether the goalkeeper had control of the ball or not.
"The referee had the perfect view of it, he was very close and he decided to give it.
"In this case you have to go with the referee, It's an unusual situation, but as long as the referee is happy with it, the goal is in.
"As a goalkeeper you make sure when you have control of the ball, you look around and make sure nobody can touch it.
"When you bounce the ball, when you don't have the ball in your hands, you don't have full control and the referee made the decision he felt was correct."
It was not the only moment of controversy in a match which saw Cech make his 300th Premier League appearance, with Jose Mourinho sent to the stands for berating the officials in the second half.
The Portuguese now faces a touchline ban.
Despite the dismissal of their manager, the Blues climbed to second in the table with a fourth win from four home games this term.
The match did not begin as planned for Chelsea, either, as a defensive lapse from David Luiz allowed Jordon Mutch to clip the ball over Cech.
The Czech Republic goalkeeper, who signed from Rennes in 2004 ahead of Mourinho's first season in charge, was hailed the world's best prior to the match, but could do nothing about the goal.
Fortunately for Chelsea there was a response and, after Hazard's equaliser, Eto'o, Oscar and Hazard were on target in the second half.
After reaching the landmark appearance, Cech has targeted many more.
"When I joined the club I wanted to become the number one goalkeeper," the 31-year-old said.
"To play 300 Premier League games is a great honour.
"If I keep my standards and level of the game the same I will have more chances to play and to get more games. It's up to me."
Chelsea play their second of five games in 15 days at Schalke on Tuesday in a crucial Champions League Group E contest.
"It's an important game," Cech said.
"We dropped three points against Basle at home, we recovered that at (Steaua) Bucharest and now we play two games with Schalke and we have to make sure we get points to help us qualify, but it will be a tough test. With two wins, it's always better."
- Sports & Recreation