Filey led the clash 2-1 with 74 minutes on the clock, goals from Daniel Marshall and Liam Sugden having them in the ascendancy for a place in the final against Hunmanby United, Sean Exley netting Pier's goal.
After violent scenes broke out among the crowd at the Flamingo Land Stadium, referee Matthew O'Brien decided to call a halt to proceedings.
Shocked Town player-boss Jordan Philliskirk said: "It's so frustrating for us as we were about 15 minutes away from getting in to a cup final, it wasn't a bad game for tackles flying in or anything and the people involved aren't associated with us.
"I've never seen anything like it, a game abandoned for trouble off the pitch, it was shocking.
"These weren't people associated with Filey Town Football Club."
Those were sentiments echoed by West Pier boss Andy Spivey, who added: "I've never seen anything like that in almost 40 years in the Scarborough League.
"It was bizarre, I'm speechless really.
"I think both West Pier and Filey Town will be keen to say that this trouble wasn't anything associated with either club."
Both clubs will now await a league ruling as to whether the result stands or not.
"The referee made a judgement call based on safety reasons, so to punish either of the clubs wouldn't make sense," added Spivey.
"We'll be enquiring as to what happens now."