Argentina superstar Lionel Messi said that his side had produced their best match of the World Cup in beating Belgium 1-0 in the quarter-finals on Saturday.
And goalscorer Gonzalez Higuain said getting off the mark with the winning goal had been a "beautiful" moment.
"We produced a very complete match. We weren't able to create that many chances, but they didn't make that many clear chances either," said Messi.
Asked if it was Argentina's most accomplished display of the tournament, the Barcelona forward told reporters: "I think it was.
"We produced a very complete match. We weren't able to create that many chances, but they didn't make that many clear chances either."
Argentina have now won their first five matches at a World Cup finals for the first time, even though they laboured in the group phase and were criticised for a lacklustre display in their 1-0 victory over Switzerland in the last 16.
It is 24 years since Argentina last reached the semi-finals of a World Cup and Messi said the team took great pride in the feat. "This is amazing," he said. "We knew it was going to be difficult.
"Argentina have gone a long time without doing this, and it was us who crossed the frontier."
Higuain's superb volley in the eighth minute of the game was enough to get Argentina through and took the Napoli striker out of a World Cup drought with his first goal of this tournament.
"Luckily it came in this match," said Higuain. "Strikers live for goals and it was a beautiful thing that it happened today."
Higuain was a substitute in Argentina's first group game and then started every match even though questions were asked about his lack of goals.
"I was calm, I did my work and I waited for it to arrive," said Higuain.
"I kept faith in my qualities and the coach and the staff were behind me. That is what matters to me. All strikers want to score, that is my job," he said.