Sarri himself, meanwhile, spoke of his wish to bring in a new forward player following the Southampton stalemate, telling a news conference: "We have to try to solve the problem of the last 15 or 20 metres".
Sarri said: "I don't know because I am not in charge of the (transfer) market and so I have to think about my responsibilities; on the pitch, in training, trying to improve my players and improve my team and improve the team's offensive phase".
The goalless stalemate at Stamford Bridge saw Arsenal close the gap on Sarri's fourth-placed side to just three points, as they seek qualification for the Champions League.More news: With or Without Facebook, Android sends data to the social network
"If they finish in there which I believe, then I think it will be a successful season for them".
Sarri, who recalled Alvaro Morata up front, saw him team dominate possession but fail to score against a Saints side which defended resolutely. "We were in control of every match recently, but it was not easy to score the first goal".
Sarri's men have scored 12 goals in their last 11 Premier League matches having managed to find the back of the net 26 times in their opening games of the season.
But Hazard couldn't do it all on his own and, while successive away wins at Watford and Palace made it a happy Christmas for Chelsea, their first home game of the new year was a lot like their last in 2018.