Conquer Club

I recently started playing this map and reached the objectives stated: the king, 6 castles, 6 nobles and 6 knights (all KO's related to the castles owned) but I didn't win, so I have now started to try and completely eliminate my opponent, is this necessary?

You need to hold them for 1 round.

I guess someone took one of those territories back before your next turn

To win a game by a victory objective you must hold the objective for one full round:
ie. You win if you still hold the objective at the beginning of your next turn.

From the instructions

Victory Conditions / Map Objectives

Some maps have 'victory' objectives, which you must conquer and hold for one round to win the game. If you are holding an objective, you will win the game at the moment you press the "Begin Turn" button, even in assassin and terminator games (think of this as the ultimate zone bonus). In team games, as with bonuses, the objective must be held by a single player.

So to answer your question you can either take the objective and hold it for one round unbroken or wipe your oppenent(s) off the map.
Does that help?

Dammit Ninja'd

That's a great help, thank you both. I didn't realise I needed to hold for a full round.