Karim Benzema scored a 29th-minute equaliser as Madrid rallied from behind to draw at home to Chelsea in the opening leg of their semi-final tie in the Spanish capital on Tuesday.
Madrid made a sluggish start at Estadio Alfredo Di Stefano, where Chelsea led after 14 minutes thanks to Christian Pulisic, though Benzema restored parity 15 minutes later.
"The return leg will be like a cup final. Their aggression and intensity, which was greater than ours, took its toll," Courtois said post-match after facing former side Chelsea, where he won two Premier League titles before leaving in 2018.
"We wanted to make the sort of start that they did and apply a high press. They gave their all. We struggled a bit more in the opening 20-25 minutes.
"We have to improve on the balls over the top. We were more in control in the second half."