Your 4th gen iPad does have the necessary software to connect to the AirPort Express but not to administer it. To do the later, you would need to install the AirPort Utility applet.
You said that your iPad can "see" the AirPort's wireless network, but can't connect. What happens exactly when you attempt to do so? Do any of your other wireless devices have any trouble connecting to the Express? Did you configure the Express for a closed network ... that is, not to broadcast its Network Name?