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The Premier League club travelled to the Alfredo Di Stefano Stadium on Tuesday for the first leg of their semi-final clash.
Christian Pulisic fired Chelsea into the lead in the 14th minute of the Champions League tie, but Karim Benzema managed to pull back an equaliser in the 29th minute.
Chelsea were frustrated not to find a winner as Courtois was in fine form against his former club.
Courtois, who left Chelsea in 2018 for Madrid, denied Timo Werner from close range early in the first half with a superb save.
But the 28-year-old Belgian shot-stopper didn't receive the warm reception he had hoped for from Tuchel at the full-time whistle.
Eagle-eyed Chelsea fans spotted the moment where Courtois extended a handshake invitation to the Blues head coach as he left the pitch.
However, Tuchel walked straight past the Los Blancos shot-stopper and embraced Antonio Rudiger and his other Chelsea players.
Courtois' fine performance keeps Madrid's hopes of reaching the final alive as Zinedine Zidane's men will play the return leg at Stamford Bridge on 5th May.
Speaking after the 1-1 draw, Tuchel admitted that Chelsea must "fight for every centimetre" in their second-leg Champions League clash with Madrid.
The 47-year-old German said: "Even if we had won here, everything is possible.
"It's half-time and we'll have to fight for every centimetre and every advantage that we want to have and we need to fight and deserve it."
Tuchel insisted that his side should have done more in the first half, saying that Chelsea could have secured a win had they capitalised on their performance.
"I have a feeling we should have won the first half and that we deserved to win the first half," he added.
"We could have perhaps decided this game in the first half an hour when we were playing so strong."
Featured Image Credit: Twitter
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