Substitute Ferran Torres scored in the second period of extra-time as Spain finally broke down 10-man Argentina at the MetLife Stadium.
Coach Luis de la Fuente's team conceded just one goal in their eight games at the 2026 tournament - the fewest by any side in a World Cup-winning campaign.
Belgium were the only team to breach their defence, in the quarter-finals in Los Angeles.
"When you don't concede, I think it's much easier to win," said Cucurella, who has recently sealed a transfer from Chelsea to Real Madrid.
"We've done an incredible job in that regard all tournament, and not just the defenders and the goalkeeper, because I think it's a team effort.
"Ultimately it's about everyone making sacrifices. We attack together and defend together. That's one of the keys to this team."
The 27-year-old left-back said Spain, who also won the World Cup in 2010, could at last switch off.
"Now it's time to celebrate," he said. "We came here with a goal, spent 50 days, or nearly 50, in camp, and now it's time to be together, enjoy every moment, reminisce, and above all, switch off.
"I think we deserve a good party."
World Cup 2026
The 2026 World Cup was held from June 11th to July 19th in the United States, Canada and Mexico. The tournament featured 48 national teams and was played in 16 modern stadiums.
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