The hosts had 72% of possession but could not find their way through a well-organised and disciplined Saints side as it ended goalless.
"I think we played a very good match for 80 metres of the pitch, then we were in trouble in the last 20 metres," said Sarri, who has Alvaro Morata as his only recognised striker with Olivier Giroud out with an ankle injury.
"We have to try to solve the problem of the last 15, 20 metres. The club knows very well my opinion. I think we need something different for characteristics.
Sarri, who dismissed the prospect of recalling strikers Michy Batshuayi and Tammy Abraham from loan spells at Valencia and Aston Villa respectively, watched his side fail to score for the second successive home league game.
For Southampton, they kept their first clean sheet in 11 Premier League games, but still dropped into the bottom three as they fall below Burnley into 18th after the Clarets' 2-1 win at Huddersfield.
Chelsea's best chance fell to Eden Hazard, but his well-hit shot was saved by Premier League debutant Angus Gunn.
Morata thought he had scored when he put the ball into the net midway through the second half, but it was ruled out as he was given offside.
Southampton offered little as an attacking force, with one Oriol Romeu shot easily saved by Kepa Arrizabalaga.
The hosts wanted a late penalty as Marcos Alonso went to ground under a challenge from Shane Long, but referee Jonathan Moss was not interested in Chelsea's appeals. SHARE THIS STORY USING ANY OF THE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW ⬇⬇⬇