The Shots' 2-0 defeat at Rotherham on Saturday confirmed their finish at the bottom of the League Two table and non-league football now beckons next season.
It brings an end to five years in League Two for the Hampshire club, and right-back Herd believes the club's players only have themselves to blame for not reaching the standards required.
"It's the worst feeling you've ever experienced, really, to be honest with you. It's just horrible, I can't really put it into words," he told Shots Player.
"So many good people at the football club deserve better and they've been let down. It's very hard to take."
Aldershot finished 11th in League Two last season, and Herd added: "I didn't stay at the football club last summer to get relegated, I would have never foreseen it. But ultimately we haven't been good enough, collectively or individually, whatever you want to call it.
"No one can argue with the fact, bottom of the pyramid, we haven't been good enough. Whether that's through ability, whether that's through attitude, I'll let other people decide. But we haven't been good enough."