Chelsea advanced to the final of the competition at the expense of the record 13-time European champions after goals in each half from Timo Werner and Mason Mount gave Thomas Tuchel’s side a 3-1 aggregate win.
But for Chelsea’s profligacy the winning margin on the night could have been wider and Zidane admits his opponents were superior over the two legs.
“They were superior, they deserved to win," Zidane told RMC Sport after Chelsea's 3-1 aggregate triumph. "They were more effective over the course of the match, they had a lot of chances too.
"Over the course of the two matches, they deserve the qualification. These are matches of a very high level, [and] we missed something tonight. It is not about organisation, even though in the duels it was difficult.
"But anyway I have said that, but I remain very proud of my players. The path they have achieved with the difficulties that we have experienced. We have to congratulate ourselves for getting here. We were one match away from the final. But tonight they were better.”
The Blues will meet Manchester City in an all-English final in Istanbul later this month while Real Madrid will turn their attention towards defending their La Liga crown as they trail leaders Atletico Madrid by two points with four matches still to play.