Italy coach Cesare Prandelli resigned after his team lost to Uruguay on Tuesday and failed to qualify for the knockout stage of the World Cup.
Giancarlo Abete, the country's football federation president, said he hoped the manager would stay on before offering his own resignation.
Italy won their first game in Brazil against England, but then lost to eventual Group D winners Costa Rica last week and were eliminated following their defeat to Uruguay.
Prandelli stepped down in his post-match news conference.
"Above and beyond, at the end of the match, I spoke to the president of the federation, and because the technical plan is under my responsibility, I have told them that I am going to resign from my position because when the technical plan and strategy fails, it is only fair for the person in question to take responsibility," Prandelli said.
"Before the renewal of my contract, there was a will. A will to continue and go ahead along an avenue, which over the past four years, has led us to somehow contain the problems of Italian football.
"After that contract, I don't know what happened in Italy, but all of a sudden we found ourselves faced with verbal aggression. We became like a political party. I've always paid my taxes and can hold my head high. I never wanted to hear that I was stealing the money of Italian taxpayers."
According to Prandelli, the game most responsible for Italy's elimination was their defeat to Costa Rica, in which striker Mario Balotelli and Italy's other attackers failed to score.
"In the technical plan, I chose [Balotelli] and now I'm resigning because it was not a winning plan," Prandelli said.
"We lost because of our performance against Costa Rica. We had the opportunity to do more. In spite of the four attackers that I fielded, something went wrong tactically. At certain levels, we have to reckon with the physical strength of the players."
Italian federation president Abete revealed he would resign, ending his tenure in August, but he said he hoped Prandelli would reconsider his decision.
"Mr. Prandelli presented his resignation. I'm going to convene a federal court meeting between Friday and Monday as soon as I go back to Italy," Abete said.
"I said to Mr. Prandelli that I hope he will withdraw his resignation because I believe above and beyond the result, which has left bitter taste in our mouths, he did his best given the levels of competitiveness that characterized our football today.
"Excellent results have been obtained and this can't be underestimated. I anticipated and told them that I will be going to the board of the federation and I will irrevocably resign, not because I feel specifically responsible for the results that have been achieved thus far, but because I want to encourage a reflection on the future strategies of the federation.
"I am dong this with a piece of mind and will continue to be engaged in sports policies. I hope he will have second thoughts, but I will not go back on my resignation."
When told that Abete would not be changing his mind, Prandelli said simply: "Neither will I."