Killick wrote off Dolphins' chances following the 2-0 defeat at Hungerford Town on Thursday but Saturday's 1-0 triumph at St Albans City has given the manager new hope.
A second-half goal from Ekow Elliott proved the difference between the sides, ensuring Poole remained within seven points of the top five with two games in hand.
Asked if Poole's play-off hopes were back on, Killick said: “I've looked at the league table and stranger things have happened.
“We have tough games left against the likes of Cambridge, Chesham and Hitchin, so it's a difficult task but we've got home games left.
“If we can reproduce the sort of performance level that we did on Saturday then we may give ourselves a fighting chance.
“Tiredness and injuries are causing us a problem but what we'd like to do is keep the whole thing going until the last game.
“Other teams might get nervous and strange results might happen. We'll just have to try and keep winning to keep the pressure on other teams and then we will see how they cope with it.”
Killick was left delighted by his team's display against a St Albans side that prior to the weekend had been on a run of six matches unbeaten.
He added: “It was an exceptional performance and result. St Albans are undoubtedly one of the best sides in the league and were playing at home, and we were very low on confidence.
“To put on the performance that we did and for the players to apply themselves in the way that they did, I thought it was a really good outcome for us.
“It gave us a much-needed boost after a period of disappointments - a bad period by our standards.”
Dolphins: Hutchings, Clarke (Martin, 83), Wannell, Dibba, Whisken, Pettefer, Brooks, Devlin (Davis, 60), Burbidge, Davies (Preston, 70), Elliott. Unused subs: Charles, Thomas (g/k).
- Meanwhile, Wimborne Town ended a run of seven Southern League games without a win as they defeated Thatcham Town 2-0 at Cuthbury.
Sam Griffin grabbed the opener shortly before the break and Mark Gamble completed victory with a penalty 17 minutes from time.
Magpies edged ahead six minutes before the break when Bufton saved from Kemble and Griffin was on hand to slam home from a narrow angle.
A Carl Evans handball gifted the home side a penalty late in the second half, with Gamble converting emphatically.
Magpies: Harvell, Arnold (Brimson, 79), Maybury, Oliver, Kemble, Blake (Grose, 81), Griffin, Davidson, Stokoe, Gamble, Webb. Unused subs: Roast.