The Swiss could have qualified from Group H if they had secured a two-goal victory against lowly Honduras but instead the match ended in a 0-0 draw.
"We had great ambitions for this match. It was too much of a burden for (the players) and it got more during the game. We got more nervous and failed to pass properly," said Hitzfeld, who was gracious in defeat though clearly stunned.
"We had to get an early goal, which we failed to do and we kept on being nervous to the very end."
He drew some consolation from the opening 1-0 victory against pre-tournament favourites Spain.
"The win against Spain is a win for eternity. That match is there to stay in the memory of all fans. Everyone will remember it for a long time," he said.
For the Central Americans, the result restored a measure of pride to a campaign in which they lost twice and failed to score any goals.
"They knew what this game meant for the nation. They really showed their courage and brought everything they had," Honduran coach Reinaldo Rueda said.
Both coaches shared a disappointment in the finishing ability of their strikers in a game that featured plenty of unfulfilled chances at both ends of the pitch.
"We lacked precision and we lacked maturity for the final strike and we did not get a goal unfortunately," Rueda said.
Hitzfeld said he was not happy with his midfield or his attackers. "We haven't lived up to our expectations. We need more strikers," he said.
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