Speaking in Brussels, Dacic said, "nobody expected this from us," EUObserver.com reported Tuesday.
Serbia was sanctioned by the United Nations during the Balkan wars in the 1990s and was bombed by NATO. Alluding to that time, Dacic called Tuesday's talks "the most important moment for Serbia since the end of World War II."
"This Cabinet took office 18 months ago and nobody expected this from us," Dacic noted. "We surprised you, because expectations were very low."
He added that "such nice words" had not been said about Serbia since the days of Josep Tito, the communist leader of Yugoslavia to which Serbia belonged before the country broke up.
Dacic declined to respond to questions about whether Serbia would eventually recognize the independence of break-away region Kosovo. However, he said "nobody in Brussels asked us to change our position" and that Belgrade would continue to seek normalization of relations with Pristina.
Serbia hopes to conclude negotiations over EU membership by 2020, Dacic said. Neighboring Croatia became an EU member state last year, ending a process that took about six years to complete.