Arriving late at Kansai Airport is not ideal in any sense. The last train connection leaves Kansai Airport at 23:14. This route is the Nankai Express to Shinimaya and then the JR from there to Osaka station (also known as Umeda).
Kansai arrival procedures can be completed in 20min if there are no queues, however you could get into troubles in case of a delay. In this event my advice would be to take a train toward Osaka and see how far you get, then use a Taxi for the last part. This is a lot cheaper than taking a Taxi all the way from Kansai Airport.
There's also a bus service that runs until late, which may be a better option. The last bus departs at 1:15 but you may have to wait sometime for it if your arrival is early. You can find the time table below.
A last option would be to change your hotel and stay the first night near Kansai Airport, there are many budget hotels in the area starting at 4,000yen a night.
I hope this helps and sorry for the bad news!