OK, so this time you would need to edit the single.php template – just like ecp-page-template.php this should initially be copied from The Events Calendar’s views directory and placed in your theme’s events directory, if you haven’t already done this.
What you will need to do is change some code at the bottom of this template – here is an example: http://pastebin.com/ikrMbrqj (you probably don’t want to copy and paste this template as is but you can use it as a guide) – if you open it in a text editor and search for “Previous Event:” you will see the amendment.