How do you counter against massive Carrier or Drone Fleet

Combo of a lot of flak frigs and carrier spam with fighter squads works pretty well generally. Also building a capship that counters bombers is something you should consider (i.e. the Kol, Halcyon or Kortul capitalships or even a Dunov could be effective using its Magnetize ability). As TEC or Vasari, building upgraded hangars also helps tremendously.

Don't forget to spam massive amounts of light frigates to kill the carriers with!

What faction are you using? 

Titan moves at same speed as carriers...so it is possible to corner them, albeit not always easy unless you are VL...

High level caps with anti-SC abilities are ideal, but not something you can always get in a pinch...fighter spam is always doable, if nothing else because you should already have a lot of carriers yourself at that stage in the game...you should always be scouting so that you know what fleet composition your opponent has...if they are spamming bombers, spam fighters (you should already have flak if you aren't VL so that you can quickly handle corvette spam) ASAP before their bombers are already on top of you...

There are some tricks you can try to pull with phase jumping...it'll drain the AM of the carriers, and a jump inhibitor may help a damaged titan escape from carriers pursuing it...also, anytime someone jumps from a well with an enemy SB, they lose all antimatter, so keep that in mind...

If you are going to go the route of abusing anti-SC cap abilities, it is often worth paying for up to level 3 on any new caps just so you have lvl 2 of the relevant ability (this is only a late game thing, don't waste money on levels early game unless it's a marza)...

Use anti air units like fighters and AAA ships. Also, research and use any AOE anti air units u have, like the Halcyon and Sentinel. Those do wonders against SC spams.

If they are bomber spamming  massing carriers carrying fighters will do(fighters counter bombers) it.  Add in some light frigates(light frigates are the best at killing the source of the strikecraft the carriers themselves) to actually hunt the carriers if you're still at a stage of the game where they won't just feed the enemy titan.

Once titans roll out if you use light frigates and how you utilize them will depend on the titan(in this case your first priority is avoiding feeding the LF to the titan- actually killing the carriers is second priority)- unless your confident of your ability to micro them and understand what sort of zones each titan threatens thought using them is risky(would be safer to just mass carriers with bombers or fighters yourself).

If you're advent, the Steal Antimatter ability can allow your Light frigates to quickly deprive the carriers of antimatter(preventing them from rebuilding destroyed strikecraft)- which can effectively remove the carriers from the fight much quicker then killing them, allowing the LF to quickly do their job then flee from the wrath of any nearby titan.  Of course any LF fleet will need to be accompanied by flak(if the enemy has a lot of fighters) or fighters of your own(if the enemy is massing bombers-  Preventing reinforcements isn't worth much unless you can kill the initial complement of strikecraft.

Ant-SC abilities help as well.  in particular  TK-push for the advent(on the Halcyon) and Weapons Jam on the Kprtul(vasari are great for buying time to kill the strikecraft.  The Vasari's defenses also sport the phasic trap which is hugely useful, if only usable defensively.

The TEC are a bit lacking in anti-SC, their only dedicated tool being the hail-mary of building a few Kols(usually a bad idea) for flak burst.  Honestly the biggest actual advantage the TEC have at antiair is the Akkan's Targetting uplink, which makes flak in particular a lot more effective(more range & negates the inherent accuracy penalty of attacking strikecraft).  But this is more handy for killing fighters then bombers since it affects your flak but not your fighters.