Your mistake is playing Dark Eldar like any other faction. The race is half-baked, but it's actually completely broken in some ways, and while it has a bunch of obvious weaknesses, the AI is way too dumb to exploit them.
I can't imagine standard multiplayer cheese not working on the AI, so instead of opening with rax + warriors, go vehicle rax + hellions, then rush the enemy base/cappers/builders with the hellions because there's virtually nothing except commanders (and I think banshees) that can survive against hellions in t1, and given that in SP you start with your own commander + honour guard, enemy commanders shouldn't be a bother. After that you get homo lab and start shitting out reaver jetbikes, go to T2, get wych cult arena + rax and start spamming the fuck out of wyches. Wyches are by far the strongest T2 infantry unit in the game, and they murder all the other dedicated T2 melees including zerks and grey knights, and just two squads can infinitely chain combat droogs. Just remember to get poison blades because it's also a broken upgrade that gives them a DPS increase of something like 50% even though it doesn't look like it. Wyches are also detectors. If somehow the AI starts fielding vehicles, you get scourges with dark lances and zap them from afar while the wyches tank - wyches can also break through vehicles pretty well if you cast corrosion on them.
In T3 you murder everything with warp beasts. You can also get taloses which are crazy strong but unreliable due to terrible pathfinding. After shitting out warp beasts, if you somehow haven't won yet, you progress to T4 and get double ravagers + the relic pimp boat. You're welcome.
DE are a stupid faction but if there's one thing that can't be said about them is that they're underpowered.