Martin Dynan’s side recovered from going 3-1 down in the 90th minute to score twice in injury time and take it to penalties – but lost 6-5 in the shootout.
It means they will be back in the Isthmian south east division next season, but they can hold their heads high, having gone so close.
Heath missed two of their spot-kicks to lose 6-5 and send Bay into a final against Ashford United.
Dynan said: “‘It’s unfortunate it’s two young boys that have missed penalties but they’re the better man than me. They’re in front of 1,100 home fans. That’s where the courage is, not scoring but stepping up. I’ve nothing but admiration for them.
“Most play-off winners tend to lose a play-off first, take experience from it, and that’s what I’m hoping the boys will do.
“They’ve been brilliant, they’ve taken me in, treated me like their own, my management team as their own and run with it.
“We’re now looking to strengthen a small squad, we’ve got to be cute with it, as we’re not big spenders like others in the league.”
Heath’s Harry Laflin and Hamish Morrison scored in injury time to secure the 3-3 draw.
Herne Bay went ahead on 15 minutes when Kieron Williams danced into the box on the left to fire a shot across Billy Collings and in off the post.
Blues winger Ibrahim Jalloh was fouled in the area, leading to Kieran Rowe’s equaliser. His penalty was saved by Bay keeper Jordan Perrin but Rowe hit the rebound in.
A minute after the restart Jack Parter restored Bay’s lead. Bay frustrated the Blues but Bay sub Edward Allsopp was sent off after the linesman spotted an elbow off the ball.
Seven minutes were added on and Laflin pounced on a bobbling ball to score from close range before Collings came up for a corner to win the ball for Tom Cadman to tee up Morrison to equalise
The goal caused ugly scenes as scuffles broke out among the crowd, players and backroom staff with teams ordered to the changing rooms by referee Scott Rudd.
It went to penalties and both teams missed one each before Cadman struck his against the bar to give Bay the win.