The 43-year-old coach saw his side beaten 6-1 by Nigeria in Belo Horizonte but said he was enormously proud of their performance.
The South Pacific side was beaten 6-1 by Nigeria in their Group B clash in Belo Horizonte, but the OFC Nations Cup champion, which is ranked 138th in the world, did the country proud as it grabbed a fine headed goal through Jonathan Tehau.
Etaeta could not hide his admiration for his side's showing, which won over neutrals in the Brazilian crowd, and confessed that he was almost overcome with emotion during the national anthems.
"I was deeply moved, almost crying," the 43-year-old told FIFA.com. "We watch World Cups on TV. Today we were participants.
"All of Tahiti was watching. Our President sent us a message and even suspended a cabinet meeting for [the game]."
Meanwhile, Marama Vahirua, the only full-time professional in the Tahiti squad, admitted he was touched by the way in which the local fans cheered his team's every touch.
"We want to thank the Brazilian fans for their support," he enthused. "It helped us to play such a great game.
"For us, it is a win to be on a pitch with Nigeria. We can be really proud of our performance today. The next game against Spain will be a dream."
Tahiti faces Spain in Rio on Thursday.