Tuchel remains unbeaten in seven games since replacing the sacked Frank Lampard last month.
But the German endured some of the same frustrations that Lampard suffered earlier in the season as the Blues domination of the ball created little, while one slack moment defensively cost them two points.
On-loan Liverpool midfielder Takumi Minamino did his parent club a favour by opening the scoring with a cool finish after sitting down Edouard Mendy and Cesar Azpilicueta on 33 minutes.
Tuchel sent on Callum Hudson-Odoi for the second-half but was less than impressed with the England international as he was replaced just 21 minutes later by Hakim Ziyech.
By that point the visitors were level as Mason Mount converted from the penalty spot after he had been chopped down by Danny Ings.
"We brought in Callum Hudson-Odoi but I was not happy with his attitude, energy and counter-pressing. I took him off and we demand 100 percent," Tuchel said.
"I feel he is not in the right shape to help us. I was not happy with his body language."
After losing six consecutive league matches for the first time in their history, even a scrappy point was a welcome boost for Southampton.
Ralph Hasenhuttl's men even came closest to a winner when Jannik Vestergaard's header looped onto the crossbar.
A draw takes Chelsea a point clear of fifth-placed West Ham United, which hosts Tottenham Hotspur on Monday (AEDT).