I'm not sure if you can do that just on the iPhone. If you're syncing between an iOS device and a computer, you could set up a smart playlist on the computer for something like "Media Kind" is Podcast and Plays is greater than zero. That'll at least help you find them.
On your iOS device, this may work: go to the "My Podcasts" pane. Press "+" to make a new station. In the Station Settings, turn "Group By Podcast" to off, Include Episodes / All, and turn "Unplayed Only" to off. Include all episodes. That should give you a list with all the episodes on your phone, and if you can scroll down that list, look at the blue dots: completely blue is unplayed; a semi-circle is started but not finished; and no circle should indicate it's been played, and those are the ones you can delete. It's clunky and there should be a better way but at the moment I can't think of one.
Alternatively: go to the My Podcasts pane. The text will tell you how many unplayed episodes there are for each podcast, but there will be nothing about played. Select the first podcast in your list, and scroll to the bottom (below the unplayed) to see if there are any played episodes. Erase them. Repeat for the second podcast on your list. If you only listen to 5 or 6 podcasts, this is manageable. If you have many more, it'd be awful.
To avoid the problem: on the iOS settings, go down to Podcasts, and set "Delete Played Episodes" to on. That'll erase played episodes after 24 hours. I think this is the route Apple wants us to take.
Note that it's unclear - or at least I don't understand - just what Podcasts does with played episodes these days. I have "Delete Played Episodes" to on, which according to Apple means it's erased after 24 hours. But then where does it go? I can't make it appear in a Station, presumably because I've got that "Delete Played Episodes" on. The only way I can find it is if I dig down into that podcast (in the "My Podcasts" pane): I can see unplayed episodes at the top, and "Played Episodes to be Deleted" below those. I don't understand why they don't just get erased, especially with them being so hard to find.