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US coach Jurgen Klinsmann announced his 23-man roster for next month's global football showdown and said Donovan, 32, was a step behind the other strikers in training camp.
"I'm disappointed. I'm sad," Donovan said. "I'm human and I wanted to go. I really wanted to go.
"I respect the decision, but I just feel in my heart that I deserve to be there and that's the pill that's hardest to swallow."
Donovan, speaking after a Los Angeles Galaxy practice session, told USA Today and the Los Angeles Times he hotly disagreed with Klinsmann's assessment of his performance and overall level.
"I think if I'm being judged based solely on what happened in camp, then I absolutely deserved to be going to Brazil," Donovan said.
That was his repsonse when asked if he thought the snub was due to personal differences between himself and Klinsmann, fueling speculation the move had more to do with strained relations than camp performance.
"I think I was one of the better players in camp," Donovan said. "If I had gone in and didn't think I deserved it then I can live with that, but that is not the case here."
"Based on my performances leading up to camp, based on my preparation for the camp, based on my fitness, based on my workload, based on the way I trained and played in camp, I not only thought I was a part of the 23, I thought I was in contention to be starting.
"So that's why all this has been pretty disappointing."
Donovan took four months off before the start of last year's Major League Soccer season, a break that saw him miss some US World Cup qualifying matches. He played a starring role for the US squad in a run to the Gold Cup last summer and returned to the national team for later qualifying matches.
Donovan, a three-time World Cup player for the US squad, has 57 goals in 156 caps and an American record five goals in World Cup matches. But he has not scored for the Galaxy in seven MLS matches this season.
Having been the standout player for the US squad in the past two World Cups, Donovan had been the face for the growing audience of American "soccer" fans.
"I'm not angry. I'm disappointed," Donovan said. "I've spent most of my adult life and the majority of my life in general dedicating myself to this sport in this country and representing my country.
"I was really looking forward to the opportunity of playing in another World Cup and helping this team. Having been in camp for 10 days, I really thought I was going to contribute in a real big way, probably bigger than I expected to at first.
"From that standpoint, I think it's disappointing. I think every one of my teammates would probably echo the same words."
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