Alberto Zaccheroni's side need a victory over the South American nation - who have already qualified from Group C - at Arena Pantanal on Tuesday to have any chance of avoiding an early exit from the tournament.
Ivory Coast occupy second spot and a point against Greece will be good enough to see them through if Japan fail to secure all three points in their final group game.
Playmaker Honda knows Japan will have to defy the odds in order to stay in the World Cup, but he insists stranger things have happened.
The AC Milan man said: "Now that we are in the critical situation, we put the past two games behind and everyone is facing forward to get ready for the next game.
"It is the World Cup that unexpected things happen and we now cannot get through on our own, but we will not give up as long as there is possibility. We are just concentrating on beating Colombia at the moment.
"Colombia are the strongest team in the group as they have already won the two games and it is really a worth challenge for us to achieve a triumph against them.
"Although they have quick and skilful players up front, we do not just stay back. It will be crucial for us to play with our style as chasing the ball down from front and keep the possession."
Honda will not ask to be kept informed of the score in the clash between Ivory Coast and Greece - who will qualify if they win and Colombia beat Japan - during the game as he focuses solely on securing his side's first victory of the tournament.
He said: "No, I am not going to put it into my mind as we will know it anyway after the game. We will just concentrate on our own game and possibly scoring two goals and achieve our biggest goal, a win."
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