Cole said the manager took a huge gamble with his treatment of the Ghanaian born England International.
During the 1-1 draw with the Saints, Tuchel only subbed on the winger at half-time, only to pull him off again just 31 minutes later.
Visibly angry Hudson-Odoi left the field and kicked a water bottle as he walked up the steps to take his place in the stands.
After Tuchel told the press that he was not happy with the 20-year-old’s performance, “I was not happy with the attitude and energy…”
Cole reacted, saying: “…I just question whether it was unnecessary at the time to upset a player that maybe is going to play for you Tuesday night.
“Maybe it was managerial genius. Maybe Callum starts on Tuesday night [Champions League against Atletico Madrid!] and he gives us the performance of his life, but he’s a fantastic young player that will be fuming at that today.
“Tuchel’s took that decision and it might be a message to his team but it’s brave as Callum is not going to be happy with that.”
Chelsea face Atletico Madrid in the first leg of their last 16 Champions League tie in Spain on Tuesday before welcoming Manchester United to Stamford Bridge on Sunday.
Tuchel is yet to taste defeat since taking over from Frank Lampard as Chelsea manager over a month ago.
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