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.
Zinedine Zidane's Madrid were unable to find a winner in a cagier second half and the Spanish powerhouse have now faced Chelsea more often than any other side in all competitions without winning in their entire history, failing to do so in four matches (D2 L2).
"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."
Benzema's goal was Madrid's solitary shot on target against Chelsea. Only versus Paris Saint-Germain in September 2019 – when they had none – have they had fewer in a Champions League game since Opta began collecting such data in 2003-04.
Meanwhile, this was the only game in which Madrid have not scored at least two goals at home this season in Champions League play. Still, they are the team who have scored the most home goals so far in the competition (14).
"With the score at 1-1, the second leg is like a cup final. I don't think it will finish 0-0," added Courtois. "They might be more relaxed about it, but I think they would be wrong to sit back.
"We caused them problems when we were in possession. We'll see what kind of game it is. When we analyse it with Zidane, we'll see what the plan is for Stamford Bridge."
Madrid head coach Zidane added: "The team have faith on what we work. That's the most important. We know our skills and trust them. We trying to do our best in each game.
"It is not easy because playing every three days different games against very good teams, like today, it is tough. But we are confident on our chances and we will try to comeback in the second leg.
"We will go to win the game, and especially, we know we need to score there."