Taking the "accentuate the positive" philosophy to the extreme, the Mexican praised the efforts of the Blue Samurai even though they trailed underdogs United Arab Emirates for 81 minutes of the contest before losing the shootout 5-4.
"I'm very proud of my team's performance," he said. "We gave everything in this 120 minutes. When the game goes to penalties, you have a 50 percent chance of winning.
"We were the better team in all aspects of the game including attack. We were careless at the start of the game which caused us to concede a goal. Then we had to fight for goals.
"I think the UAE played the match of their lives to get that result and I congratulate them."
Aguirre took over after Japan's disappointing World Cup campaign last year and the same inability to turn possession into chances and chances into goals that dogged them in Brazil was on show on Friday night.
Japan had 32 shots in the 90 minutes of normal time, the most of any team in any match at the tournament, but scored just one and two of their best attacking players, Shinji Kagawa and Keisuke Honda, missed penalties in the shootout.
"Football is a game of scoring goals and we only managed one which is why it finished 1-1," Aguirre added.
"I am happy with the number of chances we created, sometimes we missed and sometimes they stopped it. I would have been less happy if we hadn't created so many chances."
Aguirre came into the tournament under something of a cloud after allegations that he was involved in matchfixing, which he has strongly denied, surfaced in Spain.
He looks likely to retain his job for the first round of World Cup qualifying later this year, though, and said the team had shown some character on Friday.
"They won, but I think we played better football and had a more attacking mentality than them," he said.
"We showed a fighting mentality today. We need to keep this attitude in the future."
(Reporting by Nick Mulvenney, editing by Justin Palmer)
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