Saturday’s 2-0 win over Carrick Rangers saw the Sky Blues guarantee their place in the Danske Bank Premiership next season.
Jeffrey’s arrival has seen the Showgrounds club go on an impressive six-game unbeaten run, easing them away from the relegation zone and climb into seventh spot in the table.
With three games remaining they sit just one point above Dungannon Swifts, and Jeffrey insists there can be no let-up as they look to finish top of Section B.
Speaking ahead of Tuesday’s trip to basement club Warrenpoint Town, Jeffrey said: “We have ensured our place in the Premiership, but we can’t just suddenly stop now.
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“We have to look to the next challenge, and that is trying to finish top of our own ‘league’ and staying in seventh spot.
“Dungannon are right on our tails after their win against Portadown at the weekend. They are fighting to the end and we have to do the same.
“So the challenge has been thrown down to the players.”