Hazard moved to Stamford Bridge in the close-season, for a reported fee of 40 million euros.
He has already impressed for the west London club, scoring once and providing six assists for team-mates.
“Yes, I feel it but I try not to pay too much attention to it,” he said when asked about his considerable price tag.
“I know I was bought for 40 million euros. I’ve already shown at Lille, you’ve just got to do your talking on the pitch, scoring goals so that the team can win.”
“There are some great players in this team. And, of course, there are going to be teams to beat, just like last year, but I think the players we have at our disposal we can win titles and win the Champions League.”
Chelsea surrendered a 2-0 lead to draw 2-2 at home to Juventus in the Champions League on Wednesday, a result which left Hazard and his colleagues rueing their lapse in concentration.
“It’s a bit frustrating because we thought we had the match in our hands – at 2-0 you think you should manage better,” he said.
“But we were up against a good team. They’ve got good players, they made the difference. But it’s still a point, we’ll have to go looking for more points but with the quality of the group we’ll get there.”
Next up in European competition is a trip to face Danish champions Nordsjaelland, who are making their debut in the Champions League and went down 2-0 at Shakhtar Donetsk on Wednesday.
“We’ll have to be right on top of our game and stay professional,” Hazard said.
“It’s a team we don’t know much about, but if they’re champions they’ve earned their place in the Champions League.
“So we’ll have to give everything, do the maximum and go looking for points there.”