I think if the numbers are against you, your best bet MIGHT be to destroy the support ships of the enemy. I don't know the TEC and vasari support ships by heart, but while they seem like a low priority target they may prove to be quite valuable to the enemy and capable of turning the tide in your favor should they be destroyed. The next target is a little more difficult. why? And carriers tend to have VERY high shields and even with concentrated bombers attacking them they are quite resilient. Heavy fighter frigates are also a natural choice with naturally lower shields however the enemy tends to use them en masse. Going for cobalt-type frigates might be the better option.
I do like to play the advent and use the desciples to steal anti-matter from carriers so that they spawn less and in battles the AI tends to move the carriers toward the outer edge of the grav well which means less attention to you killing them.
Lastly, I love anti-fighter frigates and keep them close to my caps! That way, I can #1 spawn only bombers (though I will surely lose some to enemy fighters) and #2 by keeping anti-fighter frigs CLOSE to my caps I can minimize the damage enemyu bombers can do to them.
I have, in the past, frustrated the enemy so much with this approach that the retreated despite having larger numbers.
And easy way to NOT micromanage this is to create fleets. For example, desciples as a fleet (or more than one) to harrass enemy carriers and another fleet which has anti-fighter and protection around capital ships in CLOSE formation. With the advent, Guardians, defenders and caps with several desciples for stealing antimatter.