Harwich joint-manager Sean Tynan, in sole charge for this match with partner Matt Carmichael on holiday, made a bold start, with four trialists beginning the match.
Coggeshall were quick out of the starting blocks and in the first 30 minutes established a 3-0 lead.
Early in the second half, the Shrimpers pulled a goal back when a well-worked move finished with a neat header from Tiwa Odufuye.
Harwich had chances to reduce the arrears but Coggeshall, who narrowly missed out on promotion to the Essex Senior League last season, continued to prove formidable opponents, scoring twice more before the final whistle.
Harwich were missing some unavailable key players who will be returning and Sean (pictured) pointed out the positives that this and the other similarly testing friendlies will provide in terms of fitness and team building before finalising the starting line-up for the forthcoming league and cup programme.