The 29-year-old agreed a move to the Spanish capital last June after seven successful campaigns at Chelsea, during which time he won two Premier Leagues, a pair of Europa League titles and a PFA Players' Player of the Year award.
However, translating that success to his new club has proved challenging for Hazard, who scored only once across 10 LaLiga appearances before suffering an ankle injury last month that was likely to keep him out for the remainder of the season.
Hazard, who was sidelined between November and January with a similar problem, admitted it has hardly been a debut campaign to remember with Los Blancos, though he knows he has time to win the critics around.
"My first season in Madrid has been bad, but it's not all bad, it's a season of adaptation," he explained in an interview with RTBF.
"I'll be judged on my second season. It's a great group of players, I've met a lot of new people. It's been a great experience for me.
"I've still got four years left on my contract and I hope to be in form."
Though he only had the stitches in his ankle removed last week after undergoing surgery in Dallas, Hazard had expected to be available to represent Belgium at Euro 2020.
"I'd hoped to be fit [for the Euros] so it's a bit disappointing that they've been postponed," Hazard added.
"I'd planned to play, the operation was a few weeks ago now.
"We'll all be a year older in 2021, which is a shame, but it'll allow me to be in form.
"I think it's probably hard for the fans because they want to watch an international tournament every summer, so it's hard for them.
"But I also think that there are priorities in life that mean it had to be cancelled. Footballers are like everyone else at the end of the day. It'll wait until next year."