Atletico Madrid recorded a 3-1 win at Stamford Bridge on Wednesday to book their place in the final against city rivals Real.
Hazard, who played 90 minutes in Chelsea's loss and has been linked with a move to Paris Saint-Germain, appeared to become the latest critic of Mourinho's defensive style after the defeat.
"Chelsea is not made to play football. We're good on the counter, a little bit like Real (Madrid) against Bayern (Munich)," he told beIN Sports.
"I don't know what we lacked. After scoring, we had the game in our hands. Maybe they wanted it more than we did.
"It was an intense game, beautiful to watch with opportunities. I'm sad but logic has been respected because they deserved to qualify."
Fernando Torres looked to have put Chelsea on track with his 36th-minute goal, but Adrian levelled just before half-time.
Diego Costa and Arda Turan secured the win for Diego Simeone's side, and Hazard was left frustrated by the result.
"We did it well tonight since we scored, but their goal hurt us before the break. We failed to make the difference in the second half," Hazard said.
"Often, I'm asked to do it all by myself and it's not easy. It was a complicated game. It will be a lesson for us regarding next year."
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