Chelsea manager Thomas Tuchel said he was "very proud" after watching his players push to the "full limit" in Tuesday's Champions League quarter-final aggregate defeat to Real Madrid.
The defending European champions, needing to overturn a 3-1 first leg deficit, were 15 minutes away from completing a remarkable comeback after Timo Werner's fine solo goal gave them a 3-0 lead on the night, following earlier goals from Mason Mount and Antonio Rudiger.
However, Rodrygo levelled the tie with 10 minutes remaining before Karim Benzema struck in extra time to give Real Madrid a 5-4 aggregate victory at the Santiago Bernabeu.
After last week's first leg, Tuchel conceded that Chelsea faced a near "impossible" task in their attempt to turn the tie around but the German was full of praise for his players after narrowly missing out on the semi-finals.
"We went to the full limit today. I'm very proud of my players and I think we deserved to qualify but luck was not on our side," Tuchel said. "We were unlucky. That is why we are disappointed. We got beaten by individual quality and finishing. We made two mistakes, two ball losses. We deserved to go through after this match today. It was not meant to be.
"There are no regrets. These are the kinds of defeats you can take with pride as a sportsman. 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."
After successive damaging defeats to Brentford in the Premier League and Real Madrid last week, Chelsea have responded with an emphatic 6-0 win over Southampton and Tuesday's victory at the Bernabeu, and Tuchel believes the Blues can carry their good form forward for the rest of the season.
Real Madrid v Chelsea player ratings
"We showed a lot of courage and quality. I’m very happy, this is the way to go forward," Tuchel said. "The demand at Chelsea is very high and the players responded in a way that makes all of us proud.
"They lived up to the plan in a very different way than we did against Brentford (in a 4-1 home Premier league defeat) and in the first leg. This is the huge difference.
"We were never shy of making the point that this is the most important: how we live up to a tactic and perform in the structure. This was at the full limit today."
Ancelotti happy to 'suffer'
Real Madrid manager Carlo Ancelotti was equally proud of his players for coming through another tense Champions League tie.
Tuesday's aggregate win came five weeks after Real recovered from two goals down against Paris Saint-Germain to earn an epic 3-1 victory on the night as they knocked the visitors out 3-2 on aggregate in the last 16.
"The more I suffer, the happier I am," Ancelotti said. "It was a lot of suffering, though. We were losing 2-0 (against Chelsea) but I believe we didn't deserve it, the team did well. We were not in a hurry to score, we didn't need it, but for me when they scored the second they didn't deserve it."
Ancelotti praised his players for never giving up, adding: "We won (the tie) because we had the energy to keep the match alive. The players were brave and faced it like warriors."
"The match was difficult, we knew that, but it was more complicated. After their second goal, the team had a psychological downturn, but the magic of this stadium helps the players and the team a lot to never give up."