Hello,
That is not the purpose of the canonical tag. You should not attempt to use canonical tag to fix this sort of problem. The general purpose of the canonical tag is to filter dynamic urls to a single root page.
Example
www.myclothingstore.com/mens/t-shirts/smiley-face?size=XL&color=Red
www.myclothingstore.com/mens/t-shirts/smiley-face?size=L&color=Red
www.myclothingstore.com/mens/t-shirts/smiley-face?size=XL&color=Blue
Canonical to www.myclothingstore.com/mens/t-shirts/smiley-face
In this example the only difference of these pages is the size & color selected. The page is the same, the parameters are different. So by putting a canonical tag on this page, you help the search engine filter out the dynamic urls and rank the canonical tag.
It sounds like you may have an issue with Keyword Cannibalization, or it could simply be that your inner page is much better for the keyword then the homepage.
I'm sure somebody here would be happy to assist you further if we could take a look at the 2 pages in question and the exact keyword that you're using in Google.
Hope this helps