Coach Marcelo Bielsa said his team did not justify their status as favourites following their failure to reach the last 16.
Argentina's campaign got off to a promising start, with a 1-0 win over Nigeria.
But Argentina lost their next game to England and managed just two goals across their three fixtures.
"I feel a great sadness and disappointment," said Bielsa.
"To be favourites is a presumption prior to playing. Afterwards you have to confirm that in practice and we didn't."
Bielsa said that he was pleased with his team's performance and felt his players did not get the result they deserved.
"Today our build-up was very superior to that against
England. We had plenty of players on the end of each chance we created.
"There was no external conditions weighing on us today. We just did not get what we deserved."
The coach is soon out of contract - but gave no indication of whether he will remain in the job.
"My contract finishes at the end of the month," he said. "For
now I have nothing to say. If I have to talk about it at the time
I will do so."
Defender Javier Zanetti said his team were extremely unlucky not to qualify.
"We did everything to win, we didn't spare anything, we practically played in our opponents' half and
we're left with nothing."