With Romelu Lukaku and Timo Werner on the sidelines, Hudson-Odoi was handed a chance to impress against Norwich on Saturday and scored in the first half of the 7-0 victory.
It was Hudson-Odoi’s opening goal of the campaign and followed on from coming off the bench to replace Lukaku in the Champions League against Malmo.
Tuchel feels Hudson-Odoi can benefit from an extra push to make the most of his opportunities, the next being the visit of Southampton on Tuesday night.
“He needs that. These guys who are so full of quality hear sometimes a bit too often how good they are, but you need to prove it, to show it,” Tuchel said on Chelsea’s website.
“For the offensive guys it is easy – just read statistics and deliver assists and goals. This is what he does and what he needs to show.
“This is the highest level in England this is the highest level in Europe, so we are hopefully not unfair, but we are tough on him, because it is not enough with this talent just to be a part of the group.
“We are also very aware we are maybe a bit unfair and play him too often as a right wing-back where he cannot show his full potential.
“We are aware of that, so it is always a mix and at the moment, we think that we find a way to push him to the limits and this can change from week to week.”
Tuchel added: “He had a good game against Malmo, he had another good game on Saturday. There are still things to improve and to work on now.
“He needs to show that he is able to produce performances like this consistently and it is the time now to show that. The next opportunity is on Tuesday.”
Midfielder N’Golo Kante missed the Norwich game because of concerns over a slight muscle tightness, but should be involved against Saints.
Tuchel said: “The (Norwich) game was too early. He did the full training on Friday and after training, he said he feels his muscles a bit tight.
“He went to the physios for massages and for some treatment and he actually wanted to wait until Saturday in the morning to take the decision.
“I said no, it is such an early (kick-off time) game tomorrow, the possibility that it will change is not so high.
“I said take your time and it was simply one day too early. If the match would have been on Sunday he would have played, so he is fully available for Tuesday and for Newcastle (on Saturday).”
Chelsea finished the weekend one point clear of Liverpool at the top of the table and have also made a positive start to their Champions League defence.
Tuchel, though, feels focus needs to be on getting the best out of his squad in the next game, whatever the competition.
“I am not sure I have priorities because who says that we can select from the trophies?” the German said.
“I am more in the spirit right now that what I like about the team is when we play, we play and we push ourselves to the limit on this very special matchday – and this will be now on Tuesday against Southampton.
“I agree sometimes you can never be fully sure (with team selection) – do you interrupt a good flow? Is it better to keep everybody playing, to keep the momentum going? Or is it a moment to give some players a rest?
“We have an excellent department at Cobham who help us making these decisions, like the guys analysing, monitoring, and treating the players.
“Everybody can put their heads together and make decisions because we have had the late game on Wednesday (in the Champions League) and the early game on Saturday and now another one on Tuesday.
“So it is very likely we have some changes. At the moment I am happy that everyone who plays does so with the same style and intensity. How many changes, I do not know.”