On 7 October, Belgium national team manager Georges Leekens, citing Hazard's recent spell on the bench at Lille, said that the player needed to work harder, both physically and mentally, to regain his past year's form. The team's assistant coach, Marc Wilmots, also stated that Hazard often displayed a lazy mentality while training with the national team. Garcia responded to Leekens comments the following day stating that he thought they were "excessive" and that "Eden is only 19 years old" and can still "make more progress in all areas." Following Belgium's match against Kazakhstan, in which Hazard failed to start or even appear on the substitute's bench, Leekens responded to Garcia's comments declaring that he would stand by his previous comments and that players must think about the team and not themselves. Hazard, himself, later reflected on Leekens and Garcia comments in February 2011 stating "I learned a lot during those few weeks, mentally speaking. And since then things have got better. The national side has had a fair bit to do with that – I get a lot out of being a part of it".
Ahead of the 2011–12 season, Hazard switched to the number 10 shirt. In Lille's first competitive match of the season against Marseille in the 2011 Trophée des Champions, Hazard scored the team's second goal, which put Lille up 2–0. Marseille would later come back to win the match 5–4. On 20 August, in the team's third league match of the season, Hazard assisted on Lille's opening goal, scored by Benoît Pedretti, in a 2–1 win over Caen. A month later on 10 September, he scored two goals in a 3–1 away victory against Saint-Étienne. Fours days after, Hazard made his UEFA Champions League debut in a 2–2 group stage draw with Russian club CSKA Moscow.
After featuring as a starter in the team's 1–1 draw with Finland in February 2011, Hazard was relegated back to the substitute's bench for the team's important March 2011 UEFA Euro 2012 qualifying matches as Leekens preferred Nacer Chadli and Mousa Dembélé on the wings. In the team's 29 March qualifier against Azerbaijan, he appeared as a second-half substitute and assisted on the team's final goal in a 4–1 win. Following the matches, French media began questioning why Hazard was struggling to be appreciated in his home country, while, at the same time, was being praised in France. Marc Wilmots, assistant coach of the national team, responded to the media reports stating "Some people only see Eden's qualities" and "the French press are sometimes blinded by his moments of magic".
In Belgium's next competitive match against Turkey on 3 June 2011, Hazard started the match, but was substituted out after 60 minutes. Disappointed with his performance and substitution, the midfielder retired to the locker room and was later spotted on television outside the stadium with his family eating a hamburger while the match was still ongoing. Following the episode, which has become known as Burgergate in Belgium, Hazard apologized for the defection, while Leekens attributed Hazard's response to the substitution as "a young player making a mistake".
On 7 October 2011, nearly three years after his debut, Hazard scored his first international goal against Kazakhstan in a 4–1 victory. The victory inserted Belgium into second-place position in its group in qualifying for UEFA Euro 2012 with the team needing a victory over Germany on 11 October to secure a place in the qualifying playoffs. In the match against Germany, Hazard played the entire match as Belgium failed to earn a place in the European Championship, losing 3–1 in Düsseldorf.
Hazard primarily plays as either an attacking midfielder or a winger and has been credited as being "possibly the outstanding talent in Europe right now". At Lille under former manager Rudi Garcia, Hazard often played in the latter role in the team's 4–3–3 formation and regularly switched flanks because he could use both feet. Following the departures of fellow playmakers Yohan Cabaye and Gervinho in 2011, during the 2011–12 season, Garcia played Hazard in a creative role as a central attacking midfielder, while also allowing the player to roam back onto the wing if necessary. Two of Hazard's most common exemplary traits are his pace and technical ability, which have been described as "astonishing" and "mesmerizing". His speed, acceleration, and dribbling skills, combined with his creativity, as well as his flair, balance, agility, and low centre of gravity, courtesy of his diminutive stature (1.73 m/5 feet 8 inches), allow him to retain possession, take on defenders, and beat opponents in one on one situations.