The earthquake also cracked the spent fuel cooling pools that were located on top of the reactors. Those were leaking and a real fear at the time (I was living in Tokyo when it happened) was that if the pools emptied the spent fuel would self-ignite and we'd get a nice cloud of radioactive dust floating towards Tokyo.
The biggest thing that wasn't handled in the disaster planning was that not only was the nuclear power plant damaged, but all of the surrounding infrastructure was destroyed and a national scale disaster around the plant was happening. Japan had just gone through a massive earthquake, upwards of 20,000 people were reported dead early on and the problems at Fukushima were not the primary concern the first few days after the earthquake. The scenario for dealing with failed diesel generators would have been to truck in new generators which could have been handled before the reactors melted down in normal circumstances except it was impossible to get to the plant. The "Heavy Rescue" unit from the Tokyo fire department headed to Fukushima to help. It took them three days to get there because the roads were blocked in so many places. TEPCO was in "everything's fine, it's OK, it's OK" mode and the Japanese political level of the government was the Democratic Party of Japan who had not held power in decades and none of the political level people knew how to manage a disaster and it showed.
By the time Fukushima started receiving the kind of national level attention that it warranted the reactors were in meltdown.