Sarri, who recalled Alvaro Morata up front, saw him team dominate possession but fail to score against a Saints side which defended resolutely.
Morata had a goal disallowed and missed a decent second-half chance, continuing his frustrating form for the Blues.
“I think we played a very good match for the first 80 metres of the pitch, then we were in trouble for the last 20 metres,” said Sarri.
“We created goal opportunities, of course. But not much. It’s not easy to create opportunities in this kind of match because they (Southampton) were very compact.
“Of course if you are able to score the first goal it is easier to create opportunities.
“We have to try to solve the problem of the last 15 or 20 metres because in the last matches we were in control of the match but for us it’s not easy to score the first goal.
“So we have to solve this problem. But the performance was good.”
Asked if he thought the problem should be addressed during this month’s transfer window, head coach Sarri reiterated that he does not have control over transfers.
But the Italian, who has deployed Eden Hazard as a centre-forward in some recent matches, added that he has made his feelings known to the club’s hierarchy.
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 club knows my position, my opinion. But it depends on the board, I think, not me.”
This post was last modified on 03/01/2019