Hello and welcome to the community. 
I am afraid that you just used an incorrect approach against the starbase. The best way to deal with a starbase as a TEC player is to build Orgrov torpedo cruisers... or even better mass carriers with bomber wings. Those have the added advantage of being godlike against most things (enemy titans, capitalships... ect)
what faction was your enemy and where your TEC Loyalist or TEC Rebels? If you were TEC Loyalists, the Anklyon is a TERRIBLE assault ship and the weakest Titan in the game. Did you fight a Vasari? They have the best starbase in the game and their defense is murderous, too.
The starbase is designed to withstand its cost in your fleet cost, otherwise nobody would build one. As such brute force is not a recommended way of dealing with one..... as it likely will have far more raw power than your average fleet.
Besides having tremendous firepower and excessive health all starbases have more or less powerful special upgrades that allow them to threaten entire fleets.
TEC: The second best raw power starbase, second only the the Vasari. The upgrade Safety Override Protocol allows the use of Last Resort.... an instant self destruct of the starbase that will pulverise most things dumb enough to be in range. Second level of the upgrade does increase damage and more importantly, range. No sane enemy (note, the AI is not sane 
) will enter the explosion range of a TEC starbase.
Advent: Worst starbase in terms of raw power, however if it can use its abilities it becames nearly invulnerable. The first upgrade is Mass Disorientation, all enemys ships are cast adrift, that means that only Titans and capitalships can still use their weapons (with reduced power). All other ships can neither move nor fire and it looks hilarious, too. The second upgrade is Meteoroid Control.... which grants access to Meteor Storm. Whenever the ability is activated a meteor will hit every enemy ship in range. So if there are 100 enemy ships in range, 100 meteorids will fly and each ship will be hit by one, doing 750 raw damage on the second level. While that damage is mitigated by both shields and armor, over time it will destroy every ship not a capital or a Titan one.
The combination of those two abilites will make a fleet of hostile heavy cruiser cast adrift and then rain down fire death on them with Meteor Storm.
While the ability Meteor Storm does damage Titans and capitalships, too, those usually have more than enough armor to withstand the assault for very long ammounts of time, making the ability pretty worthless against them. It should also be noted that Mass Disorientation can be interrrupted by the enemy.
With bomber spam being the preferred way of dealing with enemy starbases the Transcenia performance against human enemies is rather poor. A smart enemy will merely fly by and destroy your starbase out of range. As Meteor Storm does damage over time and Mass Disorientation does not last forever it is usually quite possible to fly directly over the starbase with your fleet, without taking any losses.
Vasari: While not having any large area of effect (AoE) upgrades, the sheer combat power of the starbase in combination with its movement make the Orkulus by far the best starbase in the game. Equipped with deflector shields or Debris Vortex, it is more than capable of wiping most fleets effortlessly. Add a bit of support to it and the Orkulus is indeed quite unbeatable with anything but huge ammount of bombers (100+). Send your carriers moving away from it and keep them on the run, the Orkulus is a bit slower then them.
I hope that helps.
