The Premier League champions have failed to mount a substantial title defence and now face a battle to secure Champions League football for next season with a top-four finish.
Hazard, 27, called for his team mates to be united as Chelsea push towards achieving consistent results with the hopes of winning at least one trophy this season.
He said: "We need him up and running as it's goals we've struggled with". Davide Zappacosta had a chance on target, while Olivier Giroud missed a couple of chances on his first start for the club, yet made the ideal assist to make the fans enjoy the magic of Hazard as he slotted in the first of the night.
The Blues captain was quoted by the London Evening Standard as he explained to the Italian that it was imperative to give the club's ailing players a much needed break, as back-to-back defeats to Bournemouth and Watford weighed heavy on their minds.
Giroud passed up a huge opportunity to mark his Stamford Bridge bow in Chelsea blue with a goal when his weak right-footed effort was easily smothered by Ben Foster on 20 minutes.
The Blues then meet Barcelona in the Champions League next week, but have been boosted by the news that their strikers should be available.
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I have to live with this pressure until the end of the season. "We have to work and win games".
Morata's absence has hurt Chelsea in recent weeks, with the Spain worldwide aiming to recover from a back injury in time for the Champions League games versus Barcelona next week.
"We've worked a lot in training and I feel ready".
Hazard, 27, stressed that team unity will help Chelsea reach their goals.
"We must be pleased because on the same night we found Morata who played very well in the last 30 minutes, with great personality and spirit". When you lose in a bad way two game's the confidence goes down.