Rudiger, who was returning from two weeks out due to a knee problem, had to be helped from the field in the second half of Sunday's 1-1 Premier League draw away to Manchester United.
Sarri does not think the centre-back will recover in time for Thursday's trip to Frankfurt, though Willian has a chance to be fit.
"I think the most serious situation is Rudiger, with his knee," Sarri told a news conference.
"Willian at the moment is in trouble but I think it is only a knock, so we can try to recover him.
"For the next match in the Europa League, probably Antonio will be out."
Willian was forced off after a strong challenge from Marcos Rojo and Sarri felt the United defender's booking was insufficient punishment.
"Were you happy? Willian was not so happy," Sarri added after the Brazil international hurt his ankle in the tackle.
"The card was an orange card, between yellow and red. We have to accept everything from the referee, it is not easy for the referee.
"My opinion - the yellow card was not enough, of course."
David de Gea has made three errors leading to goals in his past four games in all competitions, his latest mistake allowing Marcos Alonso to cancel out Juan Mata's opener, but Sarri sympathised with the under-fire United goalkeeper.
"It can happen. He is a great goalkeeper, he is unlucky in the last period," Sarri said. "A mistake of the goalkeeper can happen.
"In general he is a very good goalkeeper, no doubt. Sometimes you have a striker who is not able to score for two months and sometimes you have a goalkeeper in difficulty for three or four matches.
"This is the job of the goalkeeper I think. It is impossible to stay at a very high level for 12 months with consistency. But he is a great goalkeeper, in my opinion."