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The Crues remain unbeaten in seven outings, but for the Sky Blues, with Jeffrey in charge for the first time, this was a first point in six matches.
Clearcut chances were at a premium, although the second half was livelier.
An 80th-minute Rodney Brown goal gave Coleraine victory over Pat McGibbon's Portadown side at Shamrock Park.
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McGibbon assumed his role as interim manager on Tuesday following the resignation of Ronnie McFall last week, with the club's record goalscorer Vinny Arkins being drafted into the backroom staff.
James McLaughlin twice tested David Miskelly in the first half as the hosts rarely looked like ending a dismal league run which had yielded just four points from their previous 10 Premiership games.
Brown ensured the Bannsiders went home with full points against the mid-Ulster club for the third time this season when Brown converted a simple finish after Jamie McGonigle had squared the ball across goal.
At Seaview, Ballymena had the better of an uninspiring first half, with Allan Jenkins firing over and David Cushley seeing his left-foot drive well saved by Sean O'Neill.
Jordan Owens, Paul Heatley and Declan Caddell went close for Stephen Baxter's side after the break, with Cushley firing wide for the visitors.
Ballymena belied the fact that they have the worst 'goals against' record in the league by defending resolutely, while the Crues have now scored just six goals in their last six league games.
This was the first time Crusaders have been involved in a goal-less game in the Premiership since December 2013.
"Every single one of my players were outstanding. They gave of their best, worked heart and showed courage," said new Ballymena manager Jeffrey after the game.
Crusaders' lead at the top of the table has been reduced to five points after the champions were held to a 0-0 draw by David Jeffrey's Ballymena United.