Goals from Abdulai Baggie and Will Spetch saw fifth-placed Poole open a seven-point gap on the chasing pack with just six games remaining.
But even if they were to finish in one of the play-off spots, Dolphins could still be barred from competing.
Although their Black Gold Stadium last week passed an FA ground-grading inspection, the National League could try to put the block on them taking part.
According to National League requirements, to participate in the play-offs, clubs must have 500 seats under cover. While this could be a stumbling block, it is believed Poole would appeal.
Killick, asked by the Daily Echo whether the uncertainty had affected his players, replied: “If our focus and mood is subdued by the prospect of not being able to compete in the play-offs, we won’t end up in the top five.
“We have to be professional and fight for every point. That’s something this group always does.
“We just have to keep on doing as well as we can. We’re not going to rule out the possibility – sometimes you hope common sense prevails. Where there’s hope, we will keep going.”
A bumper crowd turned out to celebrate Poole’s National South survival but, rather than a carnival atmosphere, a feeling of relief was the tone.
Killick added: “It was one of those games where there were a lot of people watching who were waiting to be sparked by play on the pitch, while the players perhaps needed to be sparked by the atmosphere off it.
“It never really quite got going either way. We had fleeting moments of really good play, but not enough to stir the atmosphere.”
Baggie netted his second goal of the campaign with a fine volley from a Luke Burbidge cross, a move that was the only real highlight of the opening 45 minutes. And there was even less quality on show in the second half with Poole’s second goal bundled home by makeshift striker Spetch after Luke Roberts had assisted.
Despite controlling long periods, Dolphins allowed the visitors an opportunity to spark a comeback when goalkeeper Nick Hutchings made a hash of a clearance, allowing Steve Cawley to fire into an empty net.
“Concord were always still in the game, even at 2-0,” added Killick. “I never feel comfortable but it did seem we were in good shape.
“Then, there was the mistake that allowed them to score and, as you expect, everything shifted. We weren’t brilliant but you have to give credit to the resilience shown to hold out. There is no point being too critical. We should just give credit to the players.”
Dolphins: Hutchings, Tallack, Moore, Smeeton, Whisken, Pettefer, Burbidge (Granger, 82), Devlin, Roberts, Spetch (Brooks, 65), Baggie (Cooper, 90). Unused subs: Askew, Rees (g/k).