[Strider]

Ok. Since your transport survived, and you have a Battle Report, it sounds like you hit the 'Withdrawl' button. Transports never 'survive' for failed invasions once the transport actually gets to the island and the message "Troops Ashore" appears.
With only the two Allied ships defending, your transport would have gotten to the island as long as the 'Surface' attack button was used. Also, it's very unlikely that the two Allied ships would have survived against the IJN task force you had, in a Surface Battle.

It's possible that if the 'Air' attack button was used, that neither side would have gotten any damage, and the IJN ships would have withdrawn on their own. You must use the 'Surface' attack button each combat turn, to successfully invade an island, or as the defender, to try to destroy the landing craft.