The Tigers lost the quarterfinal match against India by 109 runs at the Melbourne Cricket Ground on Thursday.
"It seems the ICC has become the Indian Cricket Council. I am not the president of the Indian Cricket Council,” Kamal told a Dhaka-based TV station.
In the 40th over of the Indian innings, Rohit Sharma pulled Rubel Hossain's full toss straight to Imrul Kayes at deep midwicket for a catch.
But on-field umpires Aleem Dar and Ian Gould signalled a height no-ball when the TV replays clearly showed the ball was below the waist-line.
Rohit Sharma, on 90 during the reprieve, went on to score his maiden World Cup century.
"Apparently, the umpires took the field against us, they have no quality,” he said.
He said he would put up the matter at the ICC's next board meeting and Bangladesh would appeal against it.
"If ICC does not probe the matter and take measures against it, I will step down as its president," he said.
"We will not accept it under any circumstances."