The defending champions lost 5-4 on penalties in the quarter-finals having forced extra time with a late Gaku Shibasaki strike, with Keisuke Honda and Shinji Kagawa both missing from 12 yards.
Defeat will place significant pressure on Aguirre's position as Japan coach, but the Mexican spoke positively about the team's display at his post-match news conference.
"I am very proud of my team’s performance," he said. "We gave everything we had over 120 minutes.
"When the game goes to penalties, it is a 50 per cent chance of winning.
"We were the better team in all aspects of the game, including attack.
"We did not take enough care at the start of the game, which caused us to concede a goal. Then, we had to fight for goals.
"The opponent won, but I think we played the better football and had a more attacking mentality than them.
"We showed a fighting mentality. We need to keep this attitude in the future."
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