West Mercia Police said four men in their 30s and 30s were detained on suspicion of possessing and setting off a flare during the game. They are from Birmingham, Hampshire and Kidderminster.
Officers identified and removed the men from the Harriers’ Aggborough Stadium and taken into custody after club stewards alerted them to the flare-throwing incident.
Superintendent Gareth Morgan said: “The majority of fans, both home and away, have enjoyed the match this afternoon and behaved respectfully towards each other before, during and after kick off.
“Unfortunately, there was a small number of home fans causing trouble, but thanks to the club’s stewards we were able to detain the four men before anyone was injured by their careless actions.
“We worked closely with the club in the build up to the game, and increased our presence around the town to ensure fans and the public were kept safe during this exciting and historic match. I would like to thank everyone involved for their co-operation.
“Sadly, it wasn’t the result we had hoped for but the match was a celebration of football, and was played in the true spirit of the FA Cup. Both the team and the community did Kidderminster proud.”
An even crueller twist was to come when the Hammers scored a last-gasp winner at the very end of extra-time with almost the last kick of the game.