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Jose Mourinho's side are already eight points adrift of leaders Manchester City after winning just one of their opening four matches.
The Blues desperately need to get back on track when they face Everton at Goodison Park on Saturday in a clash which has added intrigue following Chelsea's unsuccessful bid to sign Toffees defender John Stones.
But Hazard is one of numerous Chelsea stars who have so far failed to replicate the fine form that took them to the title last term.
And the Belgium playmaker believes that is partly due to the extra pressure of defending the title, an honour which leads opponents to raise their game to unexpectedly high levels against Chelsea.
"It's difficult to play as a champion because everyone wants to beat you, everyone wants to kill you," Hazard told fashion website HypeBeast.com.
"We wear the gold badge and... yeah, it's very good. We had a fantastic season last season... if we could do the same this season we'd be good.
"Every day I try to reach a better level. This is my job, every day I try to score. Every game I try to score.
"I just want to be champion. I just want to be a champion and win everything like I did last season."
Mourinho has had two weeks to stew on the home loss to Crystal Palace – only the second defeat in 100 home Premier League games for the manager – that ensured Chelsea entered the international break on a low.
The contrast with the start to last season could hardly be more stark.
Then, Chelsea flew out of the blocks, rising immediately to the top of the table, a position they held on to before being crowned champions in May.
- Transformed -
This time, Mourinho's side have stuttered through the opening weeks with the manager admitting his team are still short of their best.
Mourinho has pointed to last season's experience when City closed an eight-point gap in December before allowing Chelsea to break clear again as evidence of the way in which the table can be transformed.
But already the Blues are playing catch-up and a training ground injury to keeper Thibaut Courtois this week did nothing to lift the mood.
The Belgium international suffered a knee injury and faces an anxious wait before learning the full extent of the injury and is expected to miss the trip to Merseyside, with Asmir Begovic set to deputise.
Everton went into the international break on the back of a commendable 0-0 draw at Tottenham, but it came at a cost.
Midfielder Tom Cleverley will be out for between six and eight weeks with ankle ligament damage sustained in that game, while Bryan Oviedo - who played at left-back in that match - is struggling with a knee problem.
Against that backdrop, Everton manager Roberto Martinez is relieved to have kept Stones from Mourinho's clutches.
The England international had a transfer request rejected, while Everton snubbed three bids approaching £30 million ($46 million) from Chelsea, yet Martinez is confident his young centre-back will put the saga behind him with no complaints.
"John has gone from strength to strength in a period of high pressure and has used it in the right way, taking the support of everyone at the club and has performed with incredible maturity and composure," he said.
"Any story or any backlash still from the transfer window I am not going to entertain.
"Our interest is to look after every player who represents the club, they need understanding and we are going to look after the human being as well as we look after the footballer."