The Japanese were unable to break down their opponents, who were reduced to 10 men for much of the contest, and had to settle for a goalless draw.
The result means that Japan will go out of the tournament if they fail to beat Colombia in their final Group C match, with Honda calling for a more aggressive approach from his teammates.
"We lack ideas," he told reporters. "We tried to attack but we just can't put the ball in the back of the net.
"Greece were very hard to break down We have to be more aggressive against Colombia. We must somehow find a way to score goals and come away with three points."
Prior to the start of the tournament, Honda claimed that Japan would shock the world.