Brooks, 24, this week ended speculation over his future by signing a fresh one-year deal at Tatnam, despite overtures from Conference South club Sutton United.
Having scored 20 goals in two seasons, Brooks has gone from squad player to senior star with Killick keen to see another year of progress from his versatile talent.
Killick told the Daily Echo: “There was no way we could stand in the way of a full-time move but from our point of view we were relieved when he signed.
“He has become one of our most influential players and I believe he is someone who can play at a higher standard.
"Now he knows where he’s going to be next season he needs to get his head down and try to do that with us.
“If not, he needs to make sure he gets to the point where people from higher levels are looking at him, which will be inevitable if he carries on the way he is.”
Meanwhile, Killick reported no progress on his lengthy striker search but remained confident that the usual pre-season fall-out would open up Poole’s options in the coming weeks.
“We’re keeping tabs on a couple of players in different situations," he added. "We are still looking at one or two possibilities and I hope the picture will become a bit clearer now managers are starting to see what they have.
“This is the time when people come to light, both in terms of us unearthing the right players or others becoming available elsewhere.”