Fyodor Smolov got the visitors off to a flyer with a neat finish inside ten minutes, but a much-improved second half display from Real Madrid gave them a 2-1 lead before Santi Mina struck in the 85th minute to salvage a point for Celta Vigo.
In an interview with the media after the game, Hazard revealed he was happy with his display but not the result.
"I felt good," the former Lille and Chelsea man said.
"The first 10 minutes I was tired, but as the minutes went by I felt fine.
"I'm happy with my performance, but not with the result. I hope we'll improve in the next few games.”
Zinedine Zidane’s men are now one point clear of bitter rivals Barcelona at the top of La Liga, and are set to face the Blaugrana in the Clasico on March 1.
"When a team is winning 2-1 you try to see out [the match], but it wasn't to be," the 29-year-old added.
"There's still a lot of games left and we're going to fight it out until the end."
Real Madrid travel to Levante next Saturday before entertaining Manchester City in the first leg of their Champions League Round of 16 clash the following Wednesday.
