Both fungi and algae have very small cells but so do most animals. Yet both of them are visible to naked eye just like other organisms. Why do we call them as microorganisms then ?
Because both of those produce single-cells able to viably survive and grow on your own. For example, take a fungal spore and it can grow into a full fungus given enough food. I assume algae cells are the same way. In a single-cell form, fungi and algae qualify as self-sufficient microbes.
Animal cells are typically specialized and dependent on a support framework. Usually, a single animal cell left out on its own is largely doomed.