The Chelsea boss insisted the Blues’ “hands are tied” while Todd Boehly’s Stamford Bridge club purchase continues to be held up.
The Roman Abramovich era officially ended with Chelsea beating already-relegated Watford 2-1 at Stamford Bridge to cement their third-place finish.
Ross Barkley netted the final goal of Abramovich’s tenure, after 19 years and 21 trophies.
Boehly was on hand to watch the Blues complete their season, but the US magnate cannot leap into transfer action with the west Londoners still operating under a strict temporary Government licence.
The Chelsea takeover remains close to completion, with the Premier League owners and directors tests likely to be ticked off, leaving the Government to grant a new licence for the sale to proceed.
“Let’s see, when, finally, we will have the chance to act and make up, because the disadvantage in terms of timing for the rebuild is big,” said Tuchel.
“We have to be fast and smart.
“And the disadvantage grows every day, of course, while the two top teams improve their teams, and have very clear teams on which they build.
“It’s a kind of rebuild for us and makes things even more challenging.”
Russian-Israeli billionaire Abramovich put Chelsea up for sale on March 2, amid Russia’s invasion of Ukraine.
The 55-year-old was sanctioned by the UK Government on March 10, with Downing Street claiming to have proven his links to Vladimir Putin.
Chelsea have been unable to sign existing players to new deals or start recruiting new faces for next season under the terms of their temporary licence.
The Blues are understood to have a strong chance of signing Sevilla’s Jules Kounde when their position allows, but will need at least one more centre-back, with Toni Rudiger off to Real Madrid and Andreas Christensen heading to Barcelona.
“We have in the moment a huge disadvantage; that’s not decisive yet,” said Tuchel.
“There is no need to make excuses now, it is just the situation we are in and we have to be as quick as possible.
“Right now, of course, it is unsatisfying because our hands are tied and we cannot act as we want.
“We have clear ideas for the profiles and characteristic of these players.
“But it is not like you put a name on the list and then you get the player.
“You have to convince the player, you have to speak to other clubs and convince yourself this is the player, so there is normally a lot of work and it will be the same to be competitive next season, while, like everybody else, tries to close the gap to us, while the two top teams are what they are.”
Dan Gosling’s header from Adam Masina’s cross put Watford in with a shout of a point late on, before Barkley settled the tie.
Rob Edwards will take charge at Vicarage Road next term, with Roy Hodgson stepping into retirement for the second time.
While the 74-year-old has no plans to come back into management, he reserved the right to do just that, if the right opportunity came along.
“There’s always the possibility that I might be back, I don’t think I’ll ever be able to step away from football,” said Hodgson.
“I think if I’d had that ability to step away from football in my mind, then I would have done that 20 years ago.
“Football’s given me everything, and I can only say thank you to absolutely everyone who has played a part in that being the case.
“I want to say thank you and to sign off with humility.”