The Uruguayans, semi-finalists four years ago in South Africa, started without convalescent striker Luis Suarez but were still expected to deal comfortably enough with the Central Americans.
Second half goals from Joel Campbell, Oscar Duarte and Marco Urena, though, cancelled out Edinson Cavani's first half penalty and gave the "Ticos" their first ever win over the twice world champions.
Colombian Pinto said at halftime he had instructed his team to put the ball in the air to take the game to Uruguay's "strong" but "slow" players.
"Many of the things we achieved in the pitch are things I have dreamed of," he told reporters. "We won 80 percent of the aerial game. During the adverse times, we kept calm.
"The players responded very well. Today we have much more confidence and this is something very valuable in football.
"We had to be ready for war, because during war you have to face many different things. Today we were 1-0 down but the boys got the result for us."
The Costa Ricans, who have only once made it out of the group stages at a World Cup, were expected to be the makeweights in a Group D otherwise made up of former champions - Uruguay, Italy and England.
Pinto said despite their underdog status, they always had confidence in their own ability.
"Our team culture was essential," Pinto said. "This team has achieved great things. I don't think we needed to change much.
"The team showed they have the right attitude. In the first half we weren't able to go on the offensive because Uruguay wouldn't let us.
"We are facing three great teams and we will have to face them with greatness."
Striker Campbell was named man of the match after being at the heart of most of Costa Rica's best moments at the Castelao arena.
The 21-year-old drilled home the equaliser, provided the through ball for Urena's third and was the victim of the spiteful foul that saw Uruguay's Maxi Pereira dismissed.
Campbell agreed with his coach that the equanimity with which his team mates had greeted going behind had been vital to the upset.
"When we got to the changing room at half time we were all calm, no one was fighting, we knew we had to turn the result around, come what may," he told reporters.
"First we had to equalize and then look for a winner and that's how it turned out."
With one World Cup-winning country beaten, the Costa Ricans will no doubt have an extra spring in their step as they head to Recife to face Italy on June 20.
"The team was able to win because it was able to deal with going 1-0 down at the beginning of the match," Pinto said. "That's what shows how good a team this is.
"The extra confidence we gained will help us face these other rivals."