The defending champions got their defence off to an ideal start at Hunter Stadium in Newcastle, with an early Yasuhito Endo goal settling any nerves for Aguirre's men.
Shinji Okazaki and Keisuke Honda added a goal each before the break with Maya Yoshida rounding off the scoring five minutes into the second half, although Aguirre noted that certain areas still needed work.
Specifically, missed chances irked the Mexicanm, but overall he was pleased with his side's showing against a team who had to overcome air strikes, travel restrictions and other complications to debut in Australia.
"I told the players to respect all the players. This first game is the most important in the competition," he told reporters.
"We do not judge ourselves by stats on paper but rather on the pitch with what we can do. The next game is against Iraq. We will focus on what we need to do to win that game.
"The team did make mistakes but I was happy with their intensity and tonight’s outcome of four goals was pleasing.
"The main thing we achieved was to get the three points. It was not an easy game for either team due to the strong winds. I respected all the players on both teams and their playing level.
"The Palestine goalkeeper made some great saves and I wish Palestine luck for the remainder of the competition."
Experienced goalkeeper Eiji Kawashima was pleased to see Japan stay calm during Monday's win, adding that it had been a "pleasure" to play against Palestine,
"We know the first game was always going to be difficult but we scored an early goal which makes it easier to play the game," explained the Standard Liege man.
"We are confident because we were the champions last time and because we have gained a lot of experience over the past four years. We are very calm.
"The crowd in the stadium seemed happy that they saw the team on the pitch. We know the situation in Palestine and it was a pleasure to play against them."
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