From a non-technical stand point, "click" is fine. Though using the word "tap" will give the user a feeling that it is designed with them in mind, they won't notice if it isn't there.
However, from a design stand point, you should never say "click here". For instance, you would never say "To search for a topic on Google, click here" A best practice in making buttons or links in applications or webpages is to omit needless words. You would rather say, "Use Google to search for a topic." You wouldn't have a button that says "Click Here" and next it say "to submit." You would rather have a button that says "Submit." The user will know that they need to click or tap a link or button without you having to explicitly tell them.
PS - From a completely technical stand point, the programmer can use an if/else statement to test for whether the user is coming from a device with a mouse or a phone with a touch screen.
EDIT: In your edit, you give the exact sentence in question. I would suggest using as little wording as possible. Perhaps a button that simply says "Main Menu."
Though it appears we are straying from the topic of writing, I think this actually still applies. UI design, like writing, has a definitive stream of consciousness. First this, then that. Using a concept the user/reader is not used to can bring them out of the flow of the app/prose. Also, avoid being passive in your sentence. It is the difference between "The meeting will be held at 7" and "The meeting's at 7."