Check the inbox, it's the icon at the upper right of the screen that looks like a treasure chest.

Yes, start by checking your inbox. All purchases go there.

Really? I would have expected gems and silver to go straight into your totals?

Since we are talking about a shop purchase in this post, even silver goes straight into your inbox:

i

i did check my inbox

Just to be 100% clear - you're sure your purchases actually went through, right? If you check your Google Play account (or whatever Apple's equivalent is, or whatever the equivalent is if you use the PC game), you see the purchase was made?

Is there a chance that maybe your internet connection cut out or something like that, and the purchase never actually happened?

The resources in question, especially the gems, should be pretty easy to validate - either they'll be in your inbox, as Quinn mentioned, or they'll be in your inventory if you claimed them. If neither of those are true, and you also have verified that your purchase was made, you may want to open a support ticket. It's unlikely, but maybe there was a bug, or maybe someone took control of your account and spent them on your behalf.

Here is your link for the support ticket if you cannot find your store purchases anywhere, and supprot can look into it for you: 

https://mobile-support.plarium.com/hc/en-us/requests/new?ticket_form_id=360000007492