Zaccheroni's Japan side came into Tuesday's clash in Cuiaba needing a win to progress to the second round, combined with a favourable result in the match between Ivory Coast and Greece.
When Shinji Okazaki cancelled out Juan Cuadrado's early penalty on the stroke of half-time, and with Greece leading in Fortaleza, a second-half winner for Japan would have seen them through to the last 16.
As it happened, a clinical Colombia added three more goals after the interval with a brace for Jackson Martinez and one for the outstanding James Rodriguez, and Zaccheroni felt the final scoreline was harsh on his men.
"There are regrets, because we have not played well in the first two games," he said.
"Today we made a good match, the result is a liar. Today we played football.
"We had to try and go ahead. They were good on the break, we have not been lucky in the conclusion.
"But my team has a lot more shots on goal than the opposing team.
"Again, today we played a good game. I'm very happy."
