Osaze Odemwingie scored the only goal of the game in the 29th minute to cap off a bullish build-up from the right flank by Emmanuel Emenike.
But Dzeko feels his side were undone by poor officiating from New Zealand referee Peter O'Leary and his assistants, and the England-based striker did not hesitate to pour out his frustrations to KickOffNigeria.com.
"I think the referee changed the game today," Dzeko told KickOffNigeria.com after the game.
"First of all, the offside which he gave on my goal was never offside. It was not scored offside," he insisted. "It was like a minimum of half a meter between me and the Nigerian defenders, so I don't know how he gave the offside.
"The second thing, when they scored the first goal I think it was definitely a foul on our captain, and those two mistakes cost us the game."
The 28-year-old stated that him and his team-mates are disappointed with the outcome of the game, but also called for sanctions against the match officials.
"Even if we know now that we are going home, we are sad because of it. But I think the referees should go home too because what they did today, it was a shame for us, and a shame for this great competition.
The referee Peter O'Leary from New Zealand was assisted by two of his compatriots, Mark Rule and Ian-Hendrik Hintz, while Roberto Moreno Salazar of Panama was the fourth official.