South Korea suffered a narrow defeat after a costly mistake decided the match. Goalkeeper Kim Seung-gyu was unable to control a high ball under pressure early in the second half, allowing Luis Romo to score the only goal.
Despite the disappointment, Hong refused to criticise his goalkeeper and insisted his team had followed the match plan effectively.
"The goal we conceded was regrettable, but there is no need to hang our heads," Hong said. "The result is disappointing, but I believe the players executed the plans we prepared for this game well."
South Korea had expected Mexico to apply heavy pressure from the start and worked on surviving the opening stages without conceding.
"It was crucial not to concede until the 20th minute of the first half, and the players held on well," Hong explained. "After that, the game's rhythm shifted to our side, and we were able to lead in both pressing and game management."
Hong also defended Kim after the error, saying the situation involved more than just the goalkeeper's mistake.
"There was pushing between players in that scene, and I think a mistake occurred in that process," he said. "I need to review it properly before making any judgement."
The defeat left South Korea with three points from two matches, meaning their final Group A fixture against Bafana Bafana became a decisive encounter in their fight for qualification.
South Africa will face South Korea on Thursday, 25 June at 03:00 AM, with both teams needing a strong result to keep their hopes alive.
Hong warned his players they would face a difficult challenge against a South African side known for pace and attacking energy.
"South Africa is a team with good speed," Hong said. "We need to prepare tactically well."