The Belgian attacker has vowed to help the team get through their group after his first minutes for the season
Hazard helped spark the fightback with his entrance as a substitute coming prior to Karim Benzema keeping the match alive with a goal in the 87th minute before Casemiro struck the equaliser deep into stoppage time.
The Belgium international only managed one goal in 22 appearances during his debut season with Los Blancos after being troubled by injuries and had been yet to make an appearance this campaign.
Hazard was delighted to finally get back on the pitch and explained the result against Gladbach felt like a win despite the team only salvaging a point.
“I’m here to play football, so after two or three months off of the pitch, I’m so happy,” Hazard told CBS. “I just want to play football. That’s why I’m here.
“It’s like three points, but it’s not three points. We showed great character because to be 2-0 down, with just five minutes to play, I think we could score one more.
“I could score one more, but I missed, but it felt like three points, like a victory.”
Following the Gladbach result and the 3-2 defeat to Shakhtar, Real Madrid are bottom of their Champions League group with one point – however leaders Shakhtar are only three further ahead at the top.
Hazard pointed to Los Blancos’ eventual qualification after group stage struggles last season as reason why the team should still be confident of progression but warned the upcoming match against Inter will be a battle.
“[The start is] not that good, to be fair, but last year we showed after two games and one point we can go through,” Hazard said.
“We now have four games to lay, next one against Inter which is not so easy, but we are Real Madrid and we must show we can go through.”
Despite their continental struggles, Real Madrid are sitting second in La Liga after a comprehensive 3-1 in the Clasico against Barcelona at Camp Nou last weekend.