Two goals inside a quarter of an hour did the damage as Town finished second best in their First Qualifying Round replay at Bourne Stadium on Tuesday night.
The defeat extended Town’s poor record historically against the Thanet side, having failed to win any of the seven meetings between the two teams, spanning 14 years.
Jack Miles pulled one back to spark hope of a comeback, Kenny Pogue missed a great chance to make it 2-2 before half-time, only for Ramsgate to get their third early in the second half.
Jack Penny curled home Ramsgate’s first after 12 minutes, and Town went further behind 14 minutes later when Ramsgate defender George Crimmen bundled home the second following a free-kick.
Town protests that the ball went in off his hand proved in vain, and it was always going to be a
long way back after that.
Miles provided a quick boost four minutes later, thumping the ball home off the underside of the bar, sparking Town’s best spell in the game in the process.
Greg Benbow’s runs down the left started to cause problems, and one strong burst should have ended in an equaliser, only for Pogue to blast over the bar.
Town looked to build on a strong end to the first half following the restart, Rams goalkeeper Luke Watkins pouncing on a loose ball after dropping Jake McIntyre’s free-kick in his own six-yard box.
Two minutes later they conceded the third, Aaron Millbank, scorer of the Rams equaliser in the first game, guiding a looping header into the far corner.
Watkins was almost embarrassed again in the hour, rushing to the edge of the area, but Alec Fiddes’ effort was too high.
Frankie Sawyer headed another Benbow cross wide, Osman Proni’s effort was also off target - Sawyer again going close soon afterwards.
Time was against Town, but Fiddis fired wide, and substitutes Luke Coleman and Sam Crabb, both had shots blocked in a late but vain effort.
Coleman also saw his fierce strike tipped over the bar by Watkins as referee Ryan Whitaker played three minutes added time, but Town’s interest in the FA Cup was over for another season.