It's quite obvious (to me at least) why you lost.
They have:
- Lucian (senna) - this combo will always be strong, even if they nerf the units, just because of the ability to have a frontliner (lucian) that will soak up damage and they continue to do damage but can no longer take damage.
- Senna - Team buff/Enemy damage, and if she has GA or Morelo that almost doubles her power
- Soraka - Silence, AoE damage
- Jax - Stun
- Atroxx - AoE Damage
- Nasus - Tanky front-line with basically +50% health if he get's his ult... which again, more AoE damage
- Yorick - Pseudo-respawning and acts as healing and bonus attack speed for the whole team
You have:
- Twitch - Twitch without items is bad at almost any star level (he attacks slow and takes awhile to get his mana built up)... but that's a level 1 Twitch that also has almost no health... and since he's back-line, most likely the target of Soraka (on a champ that already has mana issues)
- Kog'maw - Another level 1 unit, while better than level 1 twitch, will still die fast
- Nami - ??? You have no mystic or ocean units so aside from her ult she's a dead unit. Any warden would be better in this case; at least that would buff Taric's armor.
- Skarner - Good front-line with the crystal bonus
- Rek'sai - Another good front-liner with good damage
- Taric - Being 2 star makes him considerably more valuable but the healing bonus from 6 lights can most likely out-sustain his ult
- Singed - A good unit if you can get one of the enemy units to target him, decent damage
- Ashe - Without items being displayed I have no idea how strong she is in this fight
In conclusion, they have more ways of living longer and more crowd-control tools to deal with groups of enemies while keeping themselves healthy as they die off.
I'm not sure if you've already done this but I recommend spreading your units out across the board. This 1) splits up the enemies 2) reduces the damage that AoE or bouncing damage can do. This is especially important for back-line units but it can help front-line units as well.