Single Page Apps can certainly be SEO friendly - but it needs some effort. Due to client side rendering most search engines/bots won't be able to crawl your pages. Although Google now executes JavaScript and indexes your pages, other crawlers may not do that. So, you have two options to make your SPA SEO friendly :
Use PhantomJS or a service like prerender.io to pre-render your pages so that bots can see a server rendered version.
Build Isomorphic apps - This means you need to render your pages on both client and server.
I suggest going with the second option as you get best of both the worlds in this case. I wrote a tutorial on how to build isomorphic apps using React a few months back. Take a look.
Other Resources :