Yeah, traditionally it's best to focus fire on the weaker units (like you did) rather than to focus on the bigger ones, but you maximised your win margin even further by canny maneuvers.
Amish - yeah I didn't think of that, but still, you get my point. I agree with you about fighters too. The only really efficent way to use fighters is to have plenty of them so that they have maul the enemy one run or two.
TheStarChild - maneuvering ships are important, good point. Your carriers will lurk at the rear and often will get attacks, so it's wise to lure the enemy fleet around with them while keeping them out of danger (that's against the AI anyway). Also I try and send my fighters off to whichever area has the least flak frigates, and I'm also currently experimenting with keeping all my fighters/bombers docked until the right time, say when I've destroyed the flak frigates, or taken out their fighters. Not sure how this will pan out though, still trying it.
VahnNoa - to expand on what RagingAmish said about abilities: just pick one that you think might be wise to be in control of yourself and turn off the auto-cast for every ship with that ability (eg the above mentioned Halcyon push). Then try and remember to use it in battle, get a feel for how easy to manage/unwieldy it is as well what the gains are from controlling it yourself over auto-casting. See if you want to keep on with it. If not, turn it back on.
Another important thing to think about is where you get hurt the most. If you come out of all battles totally unscathed then don't worry about it. If you find that all your