The outspoken Argentine on Sunday (Monday AEST) took aim at the "very select group" of elites he believes have commercially intruded on the World Cup.
Then, Alfaro encouraged his charges to send a message to kids on the streets of Paraguay by showing they belonged on football's grandest stage.
Alfaro made unscheduled remarks to media during training on Sunday, ahead of facing Australia on Thursday (Friday AEST) in Santa Clara.
He hoped more Paraguayans would be able to join more of the diaspora who had already turned up to support them, then hit out at the prohibitive costs standing in their way.
"People I know are having a very hard time, because travelling these days is very difficult, very expensive, the World Cups are blown out of proportion, the costs, everything else, and that's why sometimes you understand the sacrifice people make to pay for a ticket," Alfaro said.
"The essence of football is lost. And football can't be a business, it has to be football... a very select group get to enjoy it.
"Football, we all own it, primarily the poorest, because the cheapest toy to play with was a ball, which was sometimes hard to afford, but 22 people could play with just one toy.
"So the power of football is immense. And that's what we must defend."
Alfaro hasn't been afraid to speak out about different issues at the World Cup and took aim at the drinks breaks that interrupt each half.
"It's a commercial break, not a hydration break," he said.
"The game is getting out of hand."
Alfaro led Paraguay through a qualifying campaign, that included beating Argentina, Brazil and Uruguay, to their first World Cup finals since reaching the quarter-finals in 2010.
After a 4-1 defeat to the US first up, a gutsy 1-0 win over Turkey with 10 men kept Paraguay's campaign alive.
Now, Alfaro says his team, "born from adversity", will deliver a message to kids on the street back home by proving their worthiness on the field against Australia.
"Being less for us means being more," he said.
"We may eventually be less than all the teams playing here in the World Cup, but we don't feel less, we feel that if we're all together, we can somehow be more."
- With Reuters
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