The Belgian last summer swapped Chelsea for the Santiago Bernabeu in a deal worth up to £130million, but an injury-hit campaign restricted him to 21 games and just one goal.
Hazard, who had two assists in the six games he featured following the restart, could yet be fit for the resumption of the Champions League campaign in August.
He told France Info: "This year, we collectively won this league title, but I have surely had the worst season of my career individually."
He added: "It was a somewhat strange season, with everything that happened.
"The season is already very good, but I think it can be even better if we qualify in our second leg of the Champions League round of 16.
"When you play for Real Madrid, you want to win all the titles.
"The next one has to be the Champions League, although it will be difficult because we have to play in Manchester City and they have a very good team."