The 38-year-old joined the Magpies from Seaham Red Star in 1993 but will finally depart Tyneside when his contract expires at the end of the current season.
Harper is the longest-serving player in the history of the club but has largely played second fiddle to goalkeepers such as Shay Given and, more recently, Tim Krul.
"Over time you're going to have some regrets," he told BBC show 'Late Kick-off'. "The period Shay was playing year in, year out, in the early 2000s, that's when I should have done something about it.
"Ultimately I wanted to stay and play week in, week out, which I did over two, two-and-a-half years, and not many people get the opportunity to do that at such a fantastic club."
Harper conceded that the confirmation of his departure was a disappointment despite his expectation that Alan Pardew would move forward with younger members of the squad.
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"Maybe part of me was expecting it, but still when you hear it it's not nice. But that's the way the world is. We have a young, vibrant squad now, and I'm by far the oldest player."
Harper has not been offered a role in another capacity at the club by Pardew but says he would jump at the chance to return to Newcastle as a coach in the future.
"Definitely, without a shadow of a doubt - I'm well on with my coaching badges now, I have another badge in the summer and it's something I'd love to do," he added.
"But it certainly didn't crop up in the conversation with the manager, so it looks like I'll have to go to pastures new."