"Mr Onuora was relieved from his position on disciplinary grounds," Ethiopian Football Federation spokesman Melaku Ayele told Reuters.
"He was telling the newspapers that he had to clear a herd of cows off a pitch in order for the team to train. I'm not aware of a single pitch that the team trains in where you can find cows."
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Briton Onuora was appointed last June on a two year-contract and helped his side to reach the semi-finals of the regional CECAFA Cup in December, where they lost to Ivory Coast.
Ayele said the Ethiopian federation, which ended his contract on Friday, had also taken into consideration Onuora's sending-off against Madagascar in October, which led to him being banned for the game against Nigeria, and unflattering comments attributed to him by British tabloid newspapers.
Onuora, a former striker in the English lower leagues mainly for Huddersfield Town, Gillingham and Swindon Town, told state television he did not know why he had been sacked.
Ethiopia are third in their Nations Cup group, three points behind Nigeria and four behind surprise leaders Guinea.
They play Nigeria in June in Addis Ababa, before taking on Guinea and Madagascar. The Horn of Africa nation last qualified for a major tournament in 1982.
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