So, the bottom line here is that Podcasts has a compatible version for IOS 6 in App Store, but Apple does not advert this to users (unless you already have it installed on your i Pod) and make it very hard to get.
As such, you will have to use a 3rd party app to listen to podcasts, or upgrade to i OS7. The Music app is for already downloaded music, but I can't download the podcast file from the Itunes app, because it tells me I need the Podcasts app.
So what can I do, short of downloading the podcast file onto my computer and syncing my i Phone every time I want to listen to a podcast? I have an i Phone 3Gs which cannot upgrade beyond i OS 6.1.6. As others already noted, one solution is downloading a third party app.
After reading various reviews, I chose Downcast which works very well.
I'm on i OS 6 on my i Phone, and I don't like i OS 7.
When I try to listen to a podcast on the i Tunes app, it tells me to download the Podcasts app.