You need to have an RSS feed in order to podcast in the same way that you would need railroads to ride a train.
Podcasts are not defined by their content or their format as much as the way they are delivered to listeners. And this is through an RSS feed.
RSS stands for Real Simple Syndication. At its heart, RSS is just simple text files with information that is regularly updated; in this case, HTML/XML text describing your podcast. That file is usually given to a “feed reader” (in this case a podcasting app) converts the RSS text files into a digestible display of the information (the images, text, and audio associated with your podcast episode). You can learn more about the components of an RSS feed here.
If you regularly record a one-hour show and post it to the web, then it is just a series of audio files and not technically a podcast.