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Chelsea got the better chances and played the better of the two teams as both sides settled for a 1-1 draw at the Estadio Alfredo Di Stefano.
Christian Pulisic had shown composure to score a fine goal that put Chelsea in front ahead of the game against Real Madrid.
A stunning Karim Benzema strike from a set-piece later in the first half ensured that the game ended in a 1-1 draw.
Despite Chelsea’s pressure in the second half, the Blues couldn’t score against the Los Blancos.
Chelsea boss Thomas Tuchel admitted after the game that his side deserved to win the game.
Tuchel said in his post-match press conference: “We played a very strong first half, we should have won the first half.
“Unfortunately we were a bit unlucky and lacked composure and precision in the decision making in the opponents box, but we were very strong in the first half. Unfortunately we conceded a goal from a set-piece, otherwise we defended very strong throughout the whole match.
“I have the feeling that we should have won the first half, that we deserved to win the first half, and that we could have maybe decided this match very early, in the first half-an-hour when we were playing very strong. The second half was a bit of a tactical match and you could feel that we only had two days in-between two away games.”