FWIW, there is a city bus that goes from Itami Station (at least the Hankyu one, possibly the JR one as well; they are kind of far from each other) to Itami Airport, just in case someone else makes this mistake in the future. It's kind of an interesting ride, as the bus has to take the tunnel under the airport, the terminal being on the opposite side of the airport from the city of Itami.

I only know about this because I lived with a host family in Itami for a few months back in my student days...