Everything has changed as far as the AirPort Express is concerned.
Reset the device back to factory default settings and then reconfigure it again to connect to your "new" network, just like you did when you configured the Express to connect to your "old" network when you started from factory default settings.
Power up the Express for few minutes
Hold in the reset button for 10 seconds and release
Allow a full minute for the Express to restart to a slow, blinking amber light
Now you can configure the Express to connect to your new network, just like you did originally.