Even with no canonical link tags on any page, pages are likely to get indexed by Google. Many SEO tools incorrectly give that kind of error, so just stay away from such tools. The best SEO tool is Google webmaster search console. If there is any duplicate content on your site then Google search console will notify you about that in HTML improvement reports, for example same title/description across two URLs indicate that, Google have find same content across two different URL i.e. duplicate content.
Below are different URL's for Google.
If there is no any 301 redirection set, then Google might index same content on two different URL. Generally these type of duplicate content is handle automatically by Google, but there might other type of duplicate content as well, for example parameter URL, like
www.example.com/some-page?article=p2 is display same content, so Google will index both URL in search result. So Generally that kind of duplicate content might harm your SEO, but if you have already added your site on search console, then Google will gives that error on HTML improvement section. So if you don't see any error then you're fine right now.
But if you see that error, then you can implement canonical link tag on your head section. But why not implement right now?. So Google understand what URL you want to index. I highly recommended to implement canonical link tag if your site URL structure is not good, and by mistake display same content on two different URL.
Here is example of how Google use canonical link tag. For example there are two URL's in your page.
And both URL pointing to this canonical link
So when Google crawl both URL then Google will see p2 is pointing to another canonical link tag, so Google will not going to index p2 page, and will index the preferred(canonical) URL i.e. P1 page in search result.
More Reference on canonical link tag.