You are in the catch22 where the airport utility is not showing the airport express but the airport express is flashing to tell you something is wrong.
Tesserax has correctly stated that you have to fix the condition by opening it in the airport utility.. but since you have no way to do that at the moment.. the only way is by restart or reset.
So
1. Do a restart of your whole network.
Turn everything off, power up modem.. wait 2min.. power up express wait 2min.. power up one computer.. see if you can find the Express in the airport utility.. no luck power up your iphone.. and see if that will work.
Does your MBP have ethernet port.. that can also help to plug in by ethernet.. I suspect yours doesn't .. which means you need to buy a thunderbolt to ethernet adapter.. very helpful for finding stray routers.
2. No luck with the restart you then need to do reset.
First reset is soft.. press reset button for 1-2 sec..
No luck do hard reset.. press reset button for 10sec or more.. the front led will flash rapidly.
No luck do factory reset.. power off.. hold in the reset button and keep holding .. power on the express and keep holding in reset about 10sec until front LED flashes rapidly.. if you miss it.. just repeat.
Once reset the Express will appear again in the airport utility but you will need to reconfigure it.
3. If your modem is also a router.. then the express should be setup in bridge mode.. in order for this to not happen again you must set a static IP on the express .. in the Internet tab.. change from DHCP to STATIC. The current settings from the modem router will then stick on the express.. take note of this IP because you can then always find the Express by using configure other.

Type in the IP and password.
