Hessenthaler played the full 90 minutes at Kingsmeadow
Ryman League side Dover have been knocked out of the FA Cup after losing 2-0 to AFC Wimbledon on Tuesday.
The Dons won the third qualifying round replay at Kingsmeadow with goals from Tony Finn, just before half-time, and Danny Kedwell on the hour mark.
Whites manager Andy Hessenthaler told BBC Radio Kent: "I'm disappointed but we were beaten by the better side.
"It was a different story on Saturday [which ended in a 0-0 draw], we were the better side then."
We've seen where we've got to get to and we're not that far away
Andy Hessenthaler
The 42-year-old, who played the full 90 minutes, added: "It's our first real disappointment this season and we have to take it on the chin.
"We're out, it's unfortunate, but we now have to get our minds on the FA Trophy on Saturday against Staines.
"We've run them very close over the two games and listening to their reaction afterwards and the enjoyment of beating us, bearing in mind we're a league below, just shows how far we've come.
"We've seen where we've got to get to and we're not that far away."
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