The Feed Manager cannot create an excerpt from external content without removing the markup so if you use Feed Manger to create the excerpt it will not work with images.
However, if you are using Feed Manager only for consuming the rss from the internal blog feature, then there is something you can do because you can create the excerpt in the blog and then show full posts in feed manager since the full post from the blog is now an excerpt.
In the blog, if you enable excerpt on the feed in blog settings, then a new tab appears in the blog editor where you can manually create the excerpt exactly as you want it. This way your excerpt can have images and the feed manager will just use the blog excerpts as full posts, ie turn off excerpts in feed manager.
However, note also that in the blog you must create the excerpt, if you don't create it then the blog will autogenerate an excerpt but its limited in the same way as the feed manager. We don't have a good way to cut the html in half or to a specific length automatically with any sure way to not have missing closing tags or extra opening tags that could cause the page rendering to break, so any of our autogenerated excerpts are plain text only at the moment.
Hope that helps,