Morecambe had been due to visit Thornton Cleveleys in the Moore and Smalley Palace Shield Premier Division, only for the wet weather to intervene.
It was one of four matches in the division where no result was possible, meaning Morecambe picked up two points.
However, they still managed to drop a place to fourth as Euxton climbed into third with victory over Croston.
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The other match saw Eccleston move level on points with Morecambe thanks to their win against Kirkham and Wesham.
It means, with only seven games of the season remaining, four points separate second-placed Great Eccleston from fifth-placed Eccleston for the second promotion spot with Fleetwood well clear at the top.
First up for Morecambe is Saturday’s home match against sixth-placed Penwortham (1pm).
“Penwortham are a pretty decent side,” Briggs warned.
“They have three or four decent bowlers and their overseas player (Kriston Yearwood) gives it a whack.
“If he comes off then we could be in a fight but it’s a different ball game playing at our ground to Penwortham’s, which is quite small.
“If we turn up and play at our best, then I’m hoping it will be good enough for victory.
“We know the situation (in the league), it’s probably a cup final every week until the end of the season.
“We’ve just got to keep grinding out results.”
Elsewhere, rain also meant Morecambe’s second XI collected two points against Chorley.
That was also the case for Torrisholme, whose firsts were due to host Penwortham with the seconds at Ingol and Freckleton.