Although it was Costa who earned Atletico a 1-0 Champions League victory at San Siro with his 83rd-minute strike, it was the highly-rated Courtois who played arguably an even more important role in the last-16 first leg clash.
The on-loan Chelsea custodian produced a number of saves in the match, including two brilliant stops in the first half to keep out first Kaka and then Andrea Poli.
Costa said of the 21-year-old: "Courtois is one of the best goalkeepers in the world. He knows it, knows his power and he has all our confidence.
"Courtois gives us a lot and always gives us amazing help."
Atletico will now be favourites to progress through to the quarter-finals of the Champions League in next month's second leg at the Vicente Calderon, where Diego Simeone's side have won 17 of 21 matches this season and lost only once.
However, Costa is well aware the tie is not over despite their win in Italy, saying: "We know it's not done.
"We've had a good result but Milan are a great team and anything could happen in the return leg.
"We have a great advantage and we will try to keep that at the Calderon."
Atletico coach Simeone echoed those thoughts, adding: "(We're staying) absolutely calm. We know that the Champions League is difficult, it's a good step but there's still a lot to play for at the Calderon.
"The result is good but we cannot get over-confident, with a team like Milan you need to work hard to get through."