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Thomas Tuchel has criticised the referee for "smiling and laughing" with Real Madrid boss Carlo Ancelotti after Chelsea's Champions League exit.
Tuchel said he was disappointed Szymon Marciniak appeared to be having "a good time with Carlo" at the final whistle.
Trailing 3-1 from the first leg, the Blues forced extra time against the record 13-time winners at the Bernabeu before losing 5-4 on aggregate.
"I think this is the very, very worst time to do this," said Tuchel.
"After 126 minutes with one team giving their heart and desire, fighting to the very last drop.
"I know Carlo is a gentleman and a nice guy but when I wanted to go and say thank you [to the referee] I see him smiling and laughing loudly with the opponent coach.
"I think it's very, very bad timing."
Tuchel was also unhappy the official did not check the VAR monitor himself when a Marcos Alonso effort was disallowed for handball in the second half.
"If you play against Real Madrid you can maybe not expect everybody has the courage. I felt little decisions went against us also in the first leg and today as well," he said.
"I did not see the goal but I told him I'm super disappointed he didn't go to check it himself. You should stay the boss and not give decisions like this to somebody in a chair and isolated from the atmosphere.
"A referee has a certain style, things he allows and doesn't allow, so I think he should stay in charge and check it on his own, then he could explain it better.
"But this is just my opinion. Maybe it's too much to ask for in matches like this against this opponent."
Tuchel said there were "no regrets" despite Chelsea's elimination after coming close to what would have been a stunning comeback.
Many had written off Chelsea's chances, but when Timo Werner scored to make it 3-0 on the night in the 75th minute, the Blues were 15 minutes away from a sensational feat.
However, Rodrygo's volley brought the scores back level on aggregate five minutes later before Karim Benzema - a hat-trick hero at Stamford Bridge six days earlier - headed the decisive goal which sent Real through.
"These are the kind of defeats we can digest and swallow as we left nothing to regret out there," said Tuchel.
"It was not meant to be. We were simply unlucky."
"We showed the quality and character this team has and deserved to go through. There is nothing to regret."
However, the Chelsea boss was critical of the mistakes over two legs which led to Real's goals.
Benzema's extra-time goal came after Antonio Rudiger slipped in the box.
"We had a huge deficit to overcome because we did big mistakes in the first leg and today both goals come from mistakes from us," added Tuchel.
"They took advantage of the mistakes with individual quality and that was enough because over the two legs we did too many of these big mistakes."
Antonio Rudiger has scored five goals in all competitions for Chelsea this season, one more than he managed in his three previous campaigns combined
Chelsea do not have long to recover from going out of Europe as they prepare to make a second visit of the season to Wembley.
They face Crystal Palace in an FA Cup semi-final on Sunday (16:30 BST) - a competition that offers them their last chance of landing a major domestic trophy.
Despite enjoying success in the Fifa Club World Cup and Uefa Super Cup, they lost a penalty shootout to Liverpool in the Carabao Cup final and are 12 points behind leaders Manchester City in the Premier League with just eight matches left.
"The positive is we didn't give up," said defender Rudiger.
"Not many teams can come and dominate Real Madrid as we did. But over the two legs if you make these kind of mistakes like we did, you get punished.
"It was a do or die for us. I think before the game not everybody thought we would have the 3-0. For them the individual class comes to light with Luka Modric and Benzema."
Former England keeper Rob Green is worried the energy-sapping 120 minutes in Spain's capital could take its toll on Chelsea as they prepare for Wembley.
"Chelsea invested so much in the game. They put hearts and souls into this game," Green, speaking on BBC Radio 5 Live, said.
"Real Madrid looked lost. They looked like they didn't have a clue, like they were short of confidence. But they have players who produce moments."
Former England midfielder Karen Carney, speaking on 5 Live, added: "You can't complain. This leg wasn't the one that sent Chelsea out.
"They have conceded five goals over the two legs. Last season they were built on defence. You have to have a clean-sheet mentality. They leave themselves open at times."
