The Belgian, who earlier scored a free kick, wanted to take the spot kick in Chelsea's 5-1 FA Cup win over Manchester City, but instead saw the Brazilian's effort saved
Hazard scored Chelsea's fourth goal with a free kick, his first at Stamford Bridge since May 2015, by firing into the bottom corner with Willy Caballero wrong-footed, but allowed Oscar to take the spot kick.
The Brazilian's penalty was comfortably saved by Caballero, and Fabregas said Hazard should have showed the desire to score again having netted just twice all season.
"I told him: he has to take it," Fabregas told BBC Sport.
Turning to Hazard, he said: "You score one, you have to want more, man."
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Hazard admitted he wanted to take the penalty, but allowed Oscar to step up after the Brazil international had missed from the spot in a previous game.
"Yes, I want[ed] to take the penalty but Oscar I think missed the last one," he said. "OK, he missed today but it's not important, the result was already 4-1 or 5-1. It's not important."