A late goal from the prolific Diego Costa gave the Spanish title contenders a slender 1-0 advantage in their last 16 tie on Wednesday.
Milan have endured a disappointing season in Serie A, but Diego Simeone's side were made to work for their victory with Belgian goalkeeper Courtois pulling off one fine save in particular to deny Andrea Poli in the first half.
The Chelsea loanee was not shy in acknowledging praise for his performance, but warned that seven-time European champions Milan proved they are capable of causing Atletico problems in the second leg at Vicente Calderon next month.
Courtois told UEFA.com: "I feel I made a key save from Poli's header, which I managed to keep out with the help of a post.
"The second half was better for us. We went from playing with two forwards, to one with five across the middle and that gave us more control in midfield.
"There is no point in thinking that we are already through because it's going to be very hard. With an away goal they are right back in it."
Despite being wary of the threat posed by Clarence Seedorf's side, Courtois believes Atleti have proved they are capable of rolling up their sleeves and getting the job done.
"We are expecting 90 very hard minutes but, that said, you have already seen that we can deal with pressure," he added.
