How to use in-app payment without Google Play?

I downloaded the apk for the app Contacts Optimizer and had it installed via sideload. I would like to upgrade the app to PRO. This is done using an in-app payment. Trying to use this tells me that "Cannot initialize connection to in-app payment server, please try again later." I guess the reason is, because I have no Google App store on my phone. How can I use in-app payment without Google Play?