A rain-affected match saw the visitors score at a little more than a run a ball in reaching 153-5 from 25 overs.
Morecambe’s reply then saw them shot out for 89 and leapfrogged into second place in the table by Great Eccleston.
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“We bowled really poorly and fielded even worse,” the captain admitted.
“It was the bowling and fielding which let us down, it’s as simple as that.
“We had them something like 10-2 but they got to 153 which is a good score from only 25 overs.
“We had to try and keep up with the rate we needed but we were miles behind in the end.
“We weren’t good enough on the day and Eccleston deserved the win.”
Great Eccleston’s win at Croston, where they were dismissed for 81 and bowled out the hosts for 32, saw them open up a four-point lead over Morecambe.
Briggs’ players had won their previous five league and cup games before the weekend, so the skipper is hoping for the start of something similar when they visit Thornton Cleveleys on Saturday.
He added: “We pride ourselves on being able to play well at home, so we just need to go on another positive run – hopefully starting this weekend.
“After Thornton Cleveleys, we have home games against Penwortham and Kirkham and Wesham, and all three of those games are more than winnable.”