Town's FA Trophy Campaign came to an end on Tuesday night following a 3-2 defeat at Billericay.
Clinical finishes from Ricky Modeste and top scorer Callum Robinson inside the first 33 minutes saw the hosts take hold of the tie, though Simon Ainge's penalty before the interval ensured the tie was very much still alive.
The Blues regained their two goal lead nine minutes after the restart when, Cunnington fired into the top corner from the edge of the box, but the tie was not finished.
Simon Weaver made one change from Saturday's 2-2 draw as Leeds United loanee Liam Kitching made his first career senior start in place of Terry Kennedy.
Town made a bright start to the contest with Simon Ainge in the thick of the action, first the striker played through Joe Leesley whose strike was blocked, before heading George Thomson's cross just wide of the upright.
Weaver's side were having the majority of the play, but it was Ricay who took the lead in the 22nd minute as Modeste got the wrong side of Thomson and fired an unstoppable strike past James Belshaw.
Town almost levelled instantly, as they had done on Saturday, but Rob Swaine managed to get his head on Leesley's free kick to divert the delivery up onto the bar and behind.
Billericay doubled their lead 11 minutes after Modeste's clinical finish as top scorer Robinson sent a low drive into the bottom left corner from 20 yards.
Town were given the opportunity to pull a goal back from the spot five minutes later after Ainge was brought down, and the striker emphatically found the top left corner with the resulting kick.
It could have been level pegging in the last action of the half, but Thomson's fierce left footed drive flew just over the bar and saw Town behind at the interval.
The hosts restored their two goal lead nine minutes after the restart when, after Swaine's finish was cleared from the line, Cunnington sent the loose ball goal wards and, despite Belshaw getting a hand to it, couldn't keep the effort from nestling into the top corner.
With 19 minutes to play, Billericay were reduced to ten men as Callum Butcher jumped in late on Josh Falkingham just moments after picking up a yellow card, and was soon shown his second and given his marching orders.
With the man advantage Town were applying all the pressure, and almost got their reward in the 81st minute when Thomson was poked through on goal, but saw his finish blocked by Alan Julian.
Substitute Mark Beck set up a grandstand finish in the 88th minute when he converted Thomson's corner woith a glancing header, but it was too little too late as Billericay progressed to the Quarter Finals.
Harrogate Town: Belshaw, Middleton, Parker, Falkingham, Kitching, Burrell, Thomson, Emmett (Beck 79), Ainge, Knowles (Thewlis 64), Leesley
Subs not used: Swain, Cracknell, Agnew
Goals: Ainge (p) 38, Beck 88
Booked: Thomson
Billericay Town: Julian, Kizzi, Urquhart, Inman, Swaine, Deering (Paine 74), Modeste, O'Hara (Waldren 64), Butcher, Robinson (Evans 92), Cunnington
Subs not used: Bricknell, Wheeler
Goals: Modeste 22, Robinson 33, Cunnington 54
Booked: O'Hara, Butcher
Sent off: Butcher
Referee: A Quelch