Pasalic scored on the night as La Dea won 4-1 to edge the tie 4-3 on aggregate and reach the round of 16.
Costacurta was stunned by the Croatia international's performance and said: "Atalanta has joined an elite group of teams.
"Not everyone can achieve such a feat, especially given such a performance, even from an individual perspective.
"Pasalic deserves special mention. Not since Baresi in '94 have I seen a player lead a team like he did."
Costacurta was referring to Franco Baresi's amazing comeback during Italy's 1994 run to the World Cup final. The Milan great suffered a serious knee injury in the opening game, underwent surgery and made it back for the final.
The defender was the outstanding player on the pitch against Brazil, though it was the Selecao which won the final on penalties.