"I can say it is the saddest moment of my career, the pain is great because we knew we could get there, we know we had a chance to go far, to make history... But it wasn't to be this time," he wrote in an Instagram post.
Brazil were left stunned in Friday night's match in Kazan, finding themselves 2-0 down at half-time and unable to rescue the game in the second half, despite substitute Renato Augusto getting a goal back late on.
The disappointment follows Brazil's humiliating 7-1 loss against Germany in the semi-finals four years ago, when they hosted the tournament.
They played that match without Neymar, who had been stretchered off in the quarter-final win over Colombia with a fractured vertebrae.
He came to Russia having only just returned from an operation on a fractured bone in his foot in early March.
"It is difficult to find the strength to want to go back out and play football, but I am certain that God will give me sufficient strength to face up to anything," Neymar added.
"Very happy to be part of this team, I am proud of everyone. They interrupted our dream but they have not taken it from our heads or our hearts."
The forward, who became the world's most expensive player when he left Barcelona for Paris Saint-Germain last year for 222 million euros ($264 million), will be 30 by the time the next World Cup comes around in Qatar in 2022.
The Brazil squad were due to leave Russian soil on Saturday afternoon on a flight to Madrid, before carrying on to Rio de Janeiro, where they are due to arrive in the early hours of Sunday.
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