How to disable “Audio Player” to show up on the main page

The simplest solution would be to put the audio player after the read-more link.

If that would prove cumbersome (e.g. you’ve already got too may posts with audio players), you could try hooking into the the_content filter, and remove the audio player if not on a single-post view. e.g.:

function mytheme_remove_audio_player_from_home( $content ) {
    // is_singular() is true for 
    // single posts, pages, and attachments
    if ( ! is_singular() ) {
        // do something, such as a str_replace() or 
        // whatever else would be appropriate, to
        // filter out the audio player markup
    }
    return $content;
}
add_filter( 'the_content', 'mytheme_remove_audio_player_from_home' );