The Dolphins, desperate for points, were the better side for long periods at Clarence Park and took a first-half lead through Marvin Brooks.
The Saints levelled before Percy Kiangebeni bundled home the winner deep into stoppage time to leave Poole with nothing to show for their efforts.
Reliable goalkeeper Nick Hutchings was caught out for the first goal but Killick refused to point the finger at his long-serving stopper.
"It happened to Hutch on Saturday but it's happened to other players at other times,” the boss, whose side are five points adrift of safety, told the Bournemouth Echo.
"These things happen, it's just that at this stage of the season and with the situation we're in, we can't really afford to be making those sort of mistakes.
"People might find it difficult to believe given the result but we were significantly superior to the opposition and created far more chances.
"It's quite difficult to come to terms with defeat. But it's not the time to start pointing fingers. We just have to move on.”
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