The Ticos fell behind on Edinson Cavani's 24th-minute penalty, but Pinto's men hit back with three goals after the break, with the first two coming three minutes apart from Joel Campbell and Oscar Duarte.
Pinto said his squad stuck with the game strategy at the half while simply increasing their intensity.
"Our team didn't lose focus when we were down during an even and equal first half," Pinto said. "The key was the switch in speed. We blasted Uruguay's defensive line and attacked.
"We didn't alter our style of play nor our way of playing football even though we were facing a world-class rival. I had said before that we were up to the challenge of going one-on-one against any team here and we proved that today."
"We played a professional match. We didn't fall apart when we were down. Our team showed dedication but also smarts. The way a team reacts to adversity shows the quality of its players.
Costa Rica, who were without injured talisman Alvaro Saborio, had the advantage of playing Uruguay without star striker Luis Suarez, who rested his fragile ankle, but still had to deal with Edinson Cavani and Diego Forlan.
The Ticos didn't flinch in the face of celebrity, Pinto said.
"We knew how to control players like Cavani, Forlan and [Diego] Godin in their aerial game, something that is not easy to do," Pinto said.
"We won one match but that is it. The World Cup continues. There is a lot left to play and Costa Rica will keep making history."
Campbell, whom Arsenal has loaned out repeatedly, said he felt nothing but "happiness" at his team's performance on Saturday.
"Even though we went down 1-0, we stayed positive we knew we were going to win," he said. "We never thought we would lose. Thank God for the win but there are still two difficult games left.
"I was happy to score a goal. It was for my family, for all the people of Costa Rica. There are still two games left and we hope to win."