Chelsea fell short of staging one of the most remarkable comebacks in the competition's history on Tuesday at the Santiago Bernabeu.
With just ten minutes of normal time remaining, the European champions had wiped off Real Madrid's 3-1 advantage from the first leg with a 3-0 lead thanks to goals from Mason Mount, Antonio Rudiger and Timo Werner, only for Rodrygo Goes to pull one back for the hosts before Karim Benzema killed off the contest in first half extra time with a well-cushioned header.
Chelsea became just the second English team to score three goals away against Real Madrid in all European competition, after Manchester United did so in a 3-3 draw in the European Cup in May 1968.
Chelsea also had a Marcos Alonso goal ruled out by VAR for handball at 2-0.
Tuchel could not fault his charges for their elimination but pointed out individual qualities from the opposition and his side's own errors for the defeat.
"We were unlucky," he told a media conference. "That is why we are disappointed. We were beaten by individual quality and conversion. We made two mistakes, two ball losses. We deserved to go through after this match today. It was not meant to be.
"We have to reduce our amount of mistakes and we could not reduce them to a minimum over the two legs. We had two crucial ball losses.
"There are no regrets. These are the kind of defeat you can take with pride as a sportsman.
"The players lived up to the plan in a very different way that we did against Brentford and in the first leg.
"We were very disciplined on the ball and very active and invested off the ball. We showed courage and from there we showed our quality. This is the right way to do it. If we have this kind of effort, we are a special team."
