The forward says Tuesday's game panned out as Atletico predicted and labeled Thibaut Courtois one of the best goalkeepers on the planet after the 1-0 win.
The striker left it late to head in the winner for the Rojiblancos after the Rossoneri were denied numerous chances by wayward strikes or super saves from Thibaut Courtois.
Costa lauded the Belgian goalkeeper, who's spending his third season on loan at the Vicente Calderon and insisted that Diego Simeone's men will do their absolute utmost to finish the job in the second leg.
"Courtois is one of the best goalkeepers in the world and he knows it," the Brazilian-born forward told UEFA.com. "With a goalkeeper like him, we feel more secure. We know this is not finished yet, though. We have a good result but Milan are a great side and anything can happen.
"We’re not going to be over-confident. After our run of defeats people lost faith but we’ve shown how strong we are. We knew we’d have to withstand pressure and be decisive in our moment.
"Our best virtue is the bond of the team. We knew that with hard work we could get a result."
Atletico will face Clarence Seedorf's side in the second leg on March 11 at the Vicente Calderon.