The Blues’ five-game winning run under Tuchel came to an end at St Mary’s Stadium, with Mason Mount’s second-half penalty enough only for a point after Takumi Minamino’s good finish.
Southampton, who were on a six-game losing run in the league, had just 29 per cent of the ball and one shot on target.
However, they defended resolutely against a Chelsea side who failed to hit the target in the second half after Mount’s 54th-minute equaliser.
Hudson-Odoi was brought on at half-time for Tammy Abraham but was himself substituted for Hakim Ziyech after a little over half an hour in which he failed to have a shot or create a chance, completed only seven passes and did not once win back possession for his side.
Tuchel, who was animated throughout on the sidelines, confirmed the young forward was hauled off due to his apparent lack of effort as part of an attack that left the former Paris Saint-Germain coach deeply frustrated.
“We had all the chances. It would have been a deserved win, but sometimes it’s like this in football,” Tuchel told BT Sport.
“We were very, very good in the first 80 metres of the pitch but, in the last 20, I was not happy. We were not decisive enough, not aggressive enough, not clinical enough to be ahead, to create more big chances where you cannot miss.
“The decision-making was not good today. After a match like this, if you need a penalty to score once, it tells the story.
“We allowed once chance I think in the first half. There were no counter-attacks because we were high up the pitch and controlled the counter-attacks very well. For me, what was frustrating was the last 20 metres.
“We had so many opportunities, half-chances, and I had the feeling we ended our own attacks with bad choices, balls that are overhit, balls that are underhit, then we slipped, then we cannot take a two against one.
“I missed the aggressiveness and the determination in the box to finish this game early, because we had all the opportunities, but the last 20 metres was not good enough today.”
He said of his changes: “It was hard for [Abraham] to show his quality. Tammy could not put his stamp on this game, so we changed a little bit the formation.
“We brought in Hudson, but with Hudson, I was not happy with the energy, and the attitude in counter-pressing, so we decided to take him off again because we demand a lot, we demand 100 per cent, and I had a feeling he is not right in this shape where he can help us.
“It’s the decision for today. It’s a hard decision, I know, for the players to come on and off, but tomorrow it’s forgotten and he has all the possibility to start against Atletico Madrid.”
For Ralph Hasenhuttl and Southampton, effort was certainly not a concern as they won their first league point since beating champions Liverpool in January.
“It was an important point for us. We played the maximum we can at the moment,” said the Saints boss.
“I didn’t see that many chances for them and with a little more luck at the end we can win it with the header for Jannik [Vestergaard].
“It’s like a win for us today. Normally, we’re struggling after letting in an equaliser, but this time we stepped it up after 65 minutes.