Stoppage-time efforts from substitute Tom Murphy and Lee Noble saw the Darts snatch a 3-2 final-day win at the Black Gold Stadium.
Hosts Poole had led at the break after Marvin Brooks cancelled out Noble's opener before Steve Devlin's free-kick put Killick's side in control.
But, ultimately, last season's Southern League champions were condemned to defeat, a result which did not prevent a finish in the play-off berths.
Although the club had already been denied the chance to compete further by the National League and, on appeal, the Football Association, a lofty placing following promotion last term surely surpassed the expectations of even the most optimistic fan.
With a modestly-sized squad at his disposal, Killick feels his players deserves praise for their titanic effort.
He told the Daily Echo: "We're upset to lose the game as we didn't finish the season in the way we wanted to.
"But it's hard with a lack of numbers in the squad. We are running on empty but there are no changes you can make.
"This is where having inadequate strength in depth – nothing to do with subs, just numbers in terms of numbers of senior players – affects you.
"At this stage of the season, you need people. There are dips in form, there are injuries, there is fatigue and we're not in a position to make many changes.
"What people have to understand is that it's hard and that's where the players deserve amazing credit to finish fifth and defy the odds."
Dartford, already guaranteed play-off football, opened the scoring early on when Ryan Hayes's in-swinging cross was stabbed high into the net by Noble.
Back came the home side midway through the half, Brooks rising well to head home a Devlin corner with keeper Deren Ibrahim nowhere to be seen.
Six minutes before the interval, Devlin's low free-kick from an acute angle zipped across goal and nestled in the net. Advantage Poole.
The second period proved uneventful until Hutchings made a string of excellent saves midway through the half. But after Brooks was booked for diving when he had seemingly been brought down by Ibrahim in the box, the match turned.
Dartford cranked up the pressure and eventually Poole's resistance was broken, Noble's corner flicked in at the near post by Murphy.
And there was still time for Noble to lash home a dramatic winner in the sixth minute of added time, sending the visiting supporters into raptures.
Killick added: "If you reflect on the match, there are a lot of things we should have done differently. If you reflect on the season, the players can be immensely proud of what they have done."
Dolphins: Hutchings, Tallack (Leslie-Smith, 75), Smeeton, Spetch, Whisken, Pettefer (Granger, 66), Burbidge, Devlin, Roberts, Brooks, Cooper. Unused subs: Gale, Wright, Rees (g/k).