Hudson-Odoi was close to sealing a move to the Signal Iduna Park in search of more playing time.
But Tuchel's Chelsea blocked the deal on deadline day, urging the 20-year-old to challenge for a place in the match-day squad at Stamford Bridge.
"We have spoken. It was a very easy decision for me to make on the last day of the transfer period," he told reporters.
"We cannot let a player go who is in the 18/19 man squad. He is able to play as a right wing-back, a left wing-back, in the two number 10 positions. He knows the group, we know him very well. There was no chance to say yes on the last day.
"For him personally it may have been a good opportunity but for us and our targets that we want to achieve, it was simply impossible. It was an easy one for me actually.
"Callum has to overcome the gap between training and games," he said. "I see a stronger Callum every day in training and he needs to overcome this gap and show this kind of determination that he shows in training.
"If he gets minutes, it's never a gift. Nobody gets gifts because we take maybe sometimes hard decisions like for Callum not to let him go. He needs to deserve it. I know it's not his favourite position but I think he can play this position and serve the team when it's necessary.
"[Against Villa] it was necessary and still he can do better. Still he can be more aggressive, still he needs to push himself absolutely to the limits.
"This is what he does in training. He needs to overcome this gap to fight for his place in the squad. This is life at Chelsea."
Hudson-Odoi made his first appearance in Chelsea's 3-0 win over Aston Villa, having been unused substitute in the last three games.
