Tottenham did their London rivals a favour.
Bertrand Traore’s first-half goal and Anwar El Ghazi’s penalty put Villa 2-0 up before Ben Chilwell grabbed a consolation.
Cesar Azpilicueta was sent off late on for lashing out at Jack Grealish but the Blues squeezed into the top four ahead of Saturday’s Champions League final with Manchester City.
Tuchel said: “We are lucky Tottenham did the job for us. We came to win and to put any doubts to the side and it was not possible.
“We need to adjust details and we need to be spot-on on Saturday if we are going to have a positive outcome.
“I knew three or four minutes before our game was over (that they had made the top four) because the game at Leicester was over a bit earlier and it was clear we were through.
“We did not prepare for the occasion today, we prepared for the match. It’s normally hard to create chances against Aston Villa but we created a lot.
“We are still a young team and we try to evolve and make them better. We needed many clean sheets to overcome this lack of composure and precision. Today we conceded out of nothing and made it hard to come back.”
But the manager is sweating on the fitness of Edouard Mendy for the final in Porto after the goalkeeper was injured trying to stop Traore’s opener.
He added: “He fell on the frame of the net and has big pain in his ribs, we need to wait and we will have an update tomorrow. We have a week to prepare and we will see if it’s possible.”
Chelsea dominated the first half, with Mason Mount wasting their best chance when he fired over from 12 yards.
Resilient Villa held firm as the visitors dominated and stunned them by going ahead two minutes before the break.
Traore met Matt Targett’s low corner and his effort looped over Mendy to drop in off the bar, with the goalkeeper injuring himself in the process to be replaced by Kepa Arrizabalaga at the break.
The substitute’s first action was to pick the ball out of the net on 52 minutes when he was beaten by El Ghazi’s penalty after Jorginho fouled Traore.
Timo Werner then had a goal disallowed for offside as Chelsea pressed and Chilwell converted Christian Pulisic’s cross at the far post with 20 minutes left.
Emi Martinez denied him an equaliser two minutes from time and Azpilicueta was dismissed with a minute left when he lashed out at Grealish following the midfielder’s foul.
“I think the fans helped us over the line against a very good Chelsea team,” said Villa boss Dean Smith, whose side finished 11th.
“The first 20 minutes I had to count there wasn’t more than 11 of them as they seemed to get overloads all over the pitch.
“It’s been a season of progression and to finish six places and 20 points higher than we did last season is a sure sign.
“Defensively we have been outstanding and when Jack came out of the team our creativity dropped off – and that’s what we have to put right.
“There are massive positives to take from this season but we know we must get better.”