Hessenthaler came two wins from a third-straight Dover promotion
Dover will remain in the Blue Square South after losing their play-off semi-final to Woking 2-1 on aggregate.
Trailing 2-1 to Woking from Tuesday's first leg the Whites could not break down the visitors' defence as the game finished 0-0.
In front of 3,000 fans Dover hit the woodwork three times and had two efforts cleared off the line.
It means there will be no Kent club in the Blue Square Premier next season for the first time since 1986.
Dover boss Andy Hessenthaler told BBC Radio Kent: "We created some half-decent chances. We had one shot at the end, and our sub keeper John Whitehouse reckoned it went over the line, but I can't see from where I was."
"We've come second in the league, it's a fantastic achievement in our first season in the league, but it's a cruel way to go out."
"That's the structure of the league. It would have been nice if they had restructured it so that the top two go up."
Hessenthaler also announced his playing retirement after the game, after almost 25 years, which included spells with Watford, Gillingham, Hull and Barnet.
He also represented Corinthian, Dartford, Redbridge (now Dagenham & Redbridge) and his current club Dover.
"I certainly won't be playing anymore," he added. "I officially retire, you get that first. I won't be registering next year.
"I'm 45 in the summer and it's time for me to step back from playing and concentrating on winning this league."
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