The Blues progressed into the fifth round of the competition courtesy of a 1-0 victory at Stamford Bridge, with the only goal of the game coming from an Oscar free kick.
However, Mourinho was unhappy at Stoke defender Geoff Cameron's treatment of Hazard during the game and stated his belief that referee Chris Foy should have booked him earlier than he eventually did.
"Some other clubs, not just in England, especially not in England, they cry a lot with the [lack of] protection of their big players," Mourinho told PA.
"I don't want to cry, because it's not my nature, it's not Chelsea's nature. But, because Eden is small but a very strong boy and resists a lot and doesn't like to dive and doesn't like to be on the floor, opponents are coming very, very strong on him.
"Today Mr Foy was just a little bit late to give the yellow card to Cameron. It was on the third tackle. But he gave the yellow card and after the yellow card the situation was different. After that Cameron played a normal game."
Chelsea will face Manchester City at the Etihad Stadium in the pick of the FA Cup fifth-round ties.