AOK - you REALLY need to get over this 3-4 carrier thing.
1) There were 4 of them.
2) They were Advent - they cost 50% more and have 50% more squads. Again -4 Advent = 6 TEC or Vassari carriers for squad numbers.
3) They were all fighters which as stated do greater then 100% damage to a LRM.
4) He had enough that if he microd them on one ship at a time, they could pop it before shield mitigation got high enough (as Astax said).
Other things to consider
1) You have now told us you gambled on fast teching to RA (a tactic that hardly anyone uses since they changed it from a AM based ability to a resouce base one and upped the time factor). He killed your fleet before you got that ability up and running and are now complaining about how you were better in econ etc... and should have won. He was better in fleet composition and you ignored the ship that would protect your ships (flak) and protect your ships and attack his (carriers outfitted with fighters).
2) The illums MAY have had the cloning ability, which means your ships were targetting fake ones and were being killed while not killing anything
3) Malice was almost certainly in play applying additional damage accross your ships (Lvl 3 would be enough to hit almost all the ships you had in the grav well if they were close enough
4) The illums shields were being repaired
Also, did he just sit them over the top of your ships and tell them to hold position???
Post us the replay. I bet you lost 3-4 assailants before his fleet even got to you because the fighters made some passes. If you can'd do that - maybe you can record it and post it on youtube???
Ships CAN die quickly in Sins if you are off doing other stuff... That is why players like Cykur are so good - they are able to move back and forth keeping tabs on things... It is called situational awareness....
One last thing - read up on Advent Battle Ball techniques. This is a partial implementation of this tactic that you faced... It just didn't have the other caps and guardians in it....