The Stade Francais man returned to Buenos Aires alongside Juan Martin Hernandez, another of the team's key figures, as they were unable to fly back to Argentina with the rest of the squad because they had to attend the IRB Awards Ceremony.
Pichot told reporters that the team had hoped to play in the final, but were more than satisfied with their feat.
He said: "What we have achieved is very nice. We dreamt about being even higher, but we didn't play well against South Africa in the semi-final.
"Fortunately, we reacted and beat France.
"I'm proud of being the captain of this group of players. It was an honour for me. We had conviction, friendship and solidarity."
Hernandez added: "Despite the fact we were not champions, we clinched an extraordinary triumph because third place is very good. It's been a prize for the whole team.
"I truly wanted to be champion. Losing the South Africa match was painful, but the team got over it and beat France in great form."