A goal from Di Maria two minutes from the end of extra time gave the South Americans a 1-0 win to book their place in the quarter-finals.
"We have 23 heroes and the coaching staff. We gave our lives," he told reporters.
"We knew that every knockout game is like this. We knew this could happen and we did everything we could with every ball. We did everything very well.
"We had many goal situations, we always tried to play and we never got desperate. We managed it in the end and the victory is more than deserved."
Argentina will face the winners of Belgium and the USA's last-16 match.