The Belgium international received his Chelsea's player of the year award from Mourinho on Monday evening.
Although the Portuguese has praised Hazard for his improved work ethic this season, he was critical of the 23-year-old's lax marking in the Champions League semi-final second-leg loss to Atletico Madrid.
In presenting the player with his award, Mourinho said: "Next season we want more from you."
But Mourinho conceded Hazard is not alone at the club in terms of needing to improve his performance next season.
While the manager is enjoying his second spell at Stamford Bridge, he has targeted some silverware in the next campaign.
"It's good to be back but it's not good to finish third," he said. "I'm happy with the evolution, but I'm not happy with third. Next season we want to do better than we did.
"We have to do better, I have to do better, the players have to do better.
"I have great belief in them and I think next season we can start day one and we can say without any kind of fears that we are there not to fight for the title, to win it."
Hazard, whose place in Belgium's World Cup squad was confirmed on Tuesday, has confirmed he is settled at Chelsea.
Mourinho's rebuke had led to suggestions the forward may be allowed to depart this summer, with Paris Saint-Germain among the interested parties - but Hazard insists he is at home in London.
"It was a great season for me and I'm happy to play for Chelsea," he added. "I'm enjoying this city. I live in Cobham. It's easy."