The eastern European powerhouses, who impressively qualified in their group for London 2012 ahead of France, have been suggested by many as potential candidates to step onto the podium in a fortnight's time.
But Adzic, whose side face Great Britain in their opener, is keen to shift the pressure away from his side.
'Our aim is to get to the quarter-finals, this is what we are thinking about and this is what we are getting ready for,' he said.
'The spirit is good in the team, I would call it a winning spirit, so we're quite optimistic as both coaches and players.
'Our participation in London is a great success not only for our handball team but for the whole of Montenegro. We are very proud to be here.'
Montenegro are just one of the teams in action on the opening day of competition, with Russia versus Angola starting the programme in Group A.
Meanwhile, Spain take on Korea, Croatia face Brazil, Denmark clash with Sweden and Norway play France.