Costa struck his fifth goal in his last four Champions League matches in the 83rd minute on Wednesday to secure a 1-0 win at San Siro in the first leg of the last 16 clash.
However, he was quick to point to the performance of his goalkeeper as the real reason for a vital away victory.
Courtois saved well from Kaka and Andrea Poli in the first half to keep Diego Simeone's side in the game, and Costa is convinced he is world class.
"(Thibaut) Courtois is one of the best goalkeepers in the world and he knows it," said the Atletico striker. "With a keeper like him, we feel more secure.
"It was a very difficult game against a really big team. We were better at the crucial moment, however. Our best quality is our unity."
Milan dominated large parts of the match and created plenty of chances to open the scoring, particularly in the first half, before Costa punished them late on with his powerful header.
The 25-year-old expects the Serie A side to make it tough for them again in the second leg next month, and admitted that the job is only half done.
"We know that this is not finished yet," he added. "We have a good result but Milan are a great side and anything can happen.
"We are not going to be over-confident.
"After our (recent run of) defeats people lost faith in us but we have since shown how strong we are."
Atletico welcome Milan to the Vicente Calderon on March 11 looking to book their first Champions League quarter-final since 1997.
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