Rate Module: Display the rating in the comment user added to the node
I achieved a similar thing with the Fivestar module. The trick is to let the users vote when they comment. You can find a whole description for the set-up at https://drupal.org/node/1308114. Here is an adapted version of the documentation:


  Setting up the content type
  
  
  Go to admin/config/content/fivestar and create a new tag, e.g. called Vote or Rating.
  Go to your content type and add a new Fivestar field, e.g. called "Rating".
  Select the widget type Stars (rated while viewing) and tag the Rating.
  Select the number of stars. Make sure it will be the same on both the content type and the comments.
  Go to your content type's display settings and click the settings button for the Fivestar field.
  Set Value to display as stars as Average Vote.
  
  
  Setting up the comments
  
  
  Go to the comment field settings for your content type.
  Use Add existing field and add the same Fivestar field you created for the content type.
  Widget: Stars (rated while editing).
  Select the number of stars, equal to the amount that's used in your content type.
  Select the voting tag you created earlier and set the voting target to Parent Node.
  Go to the comment display settings and click the settings button for the Fivestar field.
  Set Value to display as stars as User's Vote and change Text to display under the stars to User's vote.
  


I asked a question about how to display the average rating as stars before: How to display the average rating of a node as stars in a view?. Maybe that can help you too.