The dramatic victory at the New York/New Jersey Stadium saw Ecuador recover from a difficult start to the tournament and finish among the best third-placed teams across the 12 groups.
Beccacece said the result was a moment for the entire nation to celebrate after Ecuador created a new chapter in their football history.
"Now it is time to celebrate. Time to share this feeling with your family and your friends," the Argentine coach said. "It is the biggest victory for Ecuador in a World Cup. We worked for that, we came with the dream of making Ecuador's best cup ever, and now we did."
The result was even more impressive considering Ecuador had struggled in their opening matches, losing to Ivory Coast before being held to a goalless draw by tournament debutants Curacao.
However, Beccacece insisted his team never lost belief and continued with the same tactical approach.
"We kept the tranquillity. We kept the exact same idea of how to play," he explained. "I don't think the squad deserved the previous results."
The coach also warned his players not to get carried away after the famous win over Germany.
"Football is like that: one day you win, the other day you lose. We were not in hell before, neither do I think we are in heaven now. The important thing is the balance."
Match-winner Gonzalo Plata, who played a key role in Ecuador's victory, said the experience had strengthened the squad's confidence ahead of the knockout rounds.
"It is a learning experience for us, and now we will go into the next round even more hungry for glory," Plata said. "This team believes strongly in itself. We have 26 players who will give their all for Ecuador."
Ecuador now await confirmation of their next opponent, with a potential knockout clash against co-hosts Mexico or the winner of Group L, which was expected to feature England as a possible opponent.
