Black Stars substitute Mubarak Wakaso scored a dubious second-half penalty before the Espanyol man wrapped up victory with the last kick of the game.
While Antunes admitted the result was fair, he suggested there were ‘questions’ over his side’s exit in controversial circumstances.
“The result is fair because Ghana won the play,” Antunes said.
“Today, we all watched a beautiful game but, unfortunately, the best team is going home and the tournament will lose its shine.
“This was our fourth game and in our first three games there were no questions – now there are questions. You should draw your own conclusions.
“They would want to see Ghana move into the semi-finals or do you want 200 spectators to watch Cape Verde against Togo in the semi-finals?”
Ghana boss Kwesi Appiah was pleased with his side’s effort after overcoming Cape Verde – whom he felt provided a tough test – but claimed his side lacked quality in the second half.
“Our first half was OK, but second half was not one of our best games,” Appiah said.
“Cape Verde dominated in the second half, but the important thing is that we won and are through to the semi-finals. Cape Verde proved me right that they would be tough.
“On the whole our mental attitude was really good considering the fact that in the second half Cape Verde dominated.
“We stood up to them. As for what happens next, God will decide.”
Get enhanced odds of 18/1 on Andy Murray to win Wimbledon or 10/1 on Novak Djokovic when you open a Paddy Power account.