The Greek skipper was dismissed for a second yellow in the 38th minute, leaving his side to frantically defend for the remainder of the game with Japan having 74% possession.
"When Katsouranis was sent off, it changed the game fundamentally," Santos told reporters. "Without the red card we probably could have won the game.
"I told my players at halftime that we should be compact at the back. We tried to eliminate the midfield for them and we were able to do that even though Japan were dominating."
Greece, who like Japan have one point from two games and need to beat Ivory Coast on Tuesday to maintain any chance of advancing, were unable to counter-attack as they had done, instead piling bodies at the back.
"I told my players at halftime the way to fight back is to work well defensively and try to counter-attack but you need to have the ball in the right moment to use the spaces and the wings," the Portuguese said.
"I believe we did part of that well but had difficulties in other parts."
Striker Kostas Mitroglou had to be substituted after taking a blow to his back but Santos said it may not be as serious as initially feared.
"These are very painful knocks on the bone. It is probably not severe," Santos said, offering at the same time some advice to group leaders Colombia who face Japan in their final game.
"Please don't let Japan win. That is what I have to say, I can't say anything else," he said with a loud laugh.
"We have to win (against Ivory Coast) A draw is not good enough," said Santos. "There is no other solution but to win. We must face it as we did against Russia (at Euro 2012)."
Greece had to win their last group game in that tournament to advance and they stunned group favourites Russia 1-0 to move into the last eight.
"I believe the same that happened in the Euro can happen here," he said.