During the first attempted Mongolian invasion of Japan, fighting mostly occurred on land, just after Mongolian landings. Only local landlords were there to fight, and they did not manage well. In this video we can see that Japanese fought on the beaches, but this is from a movie, probably not that much historically accurate (Mongols are using Naffatun is true, but Mongols were fighting in tight formation). No sea fights occurred, but the Mongolians feared to face larger formations and fell back to Korea.
During the second attempt, Mongols failed to land on the same position since the shogunate had built more defenses (both walls and human defenses). Mongolian fleet stood on an island in order to group with the second force of the attack. But they faced multiple attacks from Japanese small crafts, during the battle of Koan.
This put the Mongols in a difficult situation, and later the famous "kamikaze" storm put them down.
According to the wikipedia article and this source, Japanese attacked by night, on small, rowing-powered boats, and used them to close Mongoian ships and set them afire.
Question:
Why didn't Mongolians react with their bowmen, who were very well known for their capacities? They used Korean crew: didn't those crews knew how to fight such small boats?