Chelsea are third in the Premier League table, two points behind joint-leaders Manchester City and Liverpool FC.
Sarri has brought an attractive, attacking brand to Stamford Bridge which has seen them defy critics, but Kilbane firmly remains one.
The former Everton defender told Irish radio station Newstalk: “I am not getting carried away with Chelsea like a lot of people.
“It isn’t a complicated thing they’re doing right now.
“So sometimes it isn’t hard to stop. It is hard to stop Hazard.”
After finishing in the Europa League places last season in the Premier League under Antonio Conte, player and fan unrest saw Sarri come in from Napoli to buck the negativity.
He brought with him a deep-lying playmaker in Jorginho who has enabled Chelsea FC to play some of the most attractive football seen so far this season in England.
After a relatively forgiving start to the season, many expected them to come unstuck in a week which saw them face Liverpool twice.
However, they bested them in the League Cup and only a Daniel Sturridge wondergoal in the dying minutes saw Liverpool snatch a point in the league fixture on Saturday.
With these results, they have reinforced their title credentials in the eyes of many, but not everyone.
Kilbane perhaps knows something that Jurgen Klopp does not, but does sympathise with the German trying to stop Eden Hazard.
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