The Spaniards make the trip to the San Siro for the first leg of their Champions League last 16 tie on Wednesday having bounced back from their second league defeat of the season at Almeria by beating Real Valladolid 3-0 on Saturday night.
That was Atletico's third victory in four league games and lifted them level on 60 points with Barcelona and Real Madrid at the top of the Primera Division standings.
Milan, in contrast, have struggled domestically and are down in ninth place in Serie A, 31 points behind league leaders Juventus.
However, Atletico would be foolish to take the seven-time European champions lightly, according to Costa.
"We expect a very difficult but beautiful game at the San Siro," he told www.marca.com.
"In order to achieve something positive, we will need to do our best. Milan have a lot of tradition and know how to play these type of games. We will have do a great job against them."
Atletico, coached by Diego Simeone, have advanced to the knockout phase of the competition for the first time since the 2008-09 campaign and have not progressed to the quarter-final stages since 1997.
"We know how much this game means for Atletico and our fans," Costa said.
"This is a big game for us and Atletico is a top team that has to play in these type of games."
Costa, who scored four goals in three games to help the team finish top of their Champions League group, sees AC Milan striker Mario Balotelli as his team's biggest threat.
"Balotelli is one of the best strikers in the world," Costa said.
"Our defenders know this and will keep a close eye on him."
Balotelli scored his 10th league goal in Friday's 1-0 triumph over Bologna.
The outcome allowed the Rossoneri to bounce back from their 3-1 defeat at Napoli, Milan's first league loss under coach Clarence Seedorf.
The former Real Madrid and Milan midfielder was appointed after the dismissal of Massimiliano Allegri last month despite having no coaching experience.
Seedorf, who won the Champions League four times as a player, is confident his team can deliver against Atletico.
"Atletico have been playing at a high level for the past two seasons," Seedorf said.
"They are in good form but we have a chance to do well. Champions League games are special and we will try to take advantage of Atletico's weaknesses.
"We respect them but we will try to give our all. The team has worked well in training and I'm confident we can do well."
The hosts are without midfield pair Sulley Muntari and Riccardo Montolivo, both suspended, while forwards Stephan El Shaarawy and Robinho are among six players out injured.
Milan travel to the Vicente Calderon stadium for the return leg on Mach 11.