The problem may be that the AirPort Express does not support your printer model. Not all printers are supported, and Apple tends to favor popular, lower priced All-in-One devices for USB support.
On your Mac....open System Preferences (gear icon on the dock)
Open Print & Scan
Click the + (plus) button at the bottom of the printer list
Hopefully, your printer model will appear. If it does, click on the name of the printer to highlight it, then click Add to install the printer at the location of the AirPort Express
Try to print. Be sure to select the correct location of your printer, as it may appear as a printer connected to your MacBook Pro and as a printer connected to the AirPort Express. You must choose the correct location to be able to print.
If your printer model does not appear when you click the + button in the steps above, about all that you can do is contact HP Support to see if they have an updated printer driver that you could download and install....that might allow the print function at the AirPort Express.