First off I'm going to shamelessly invite you to our Proving Grounds Discord; a great place to discuss strategy. I've seen you start many posts of this nature and I think you'll be well served by our strategy discussion channel.
https://discord.gg/TRCa8WRSecondly; to answer the question. Chaos vs Eldar is very commander dependant, each Chaos commander has at least one tool to really put the hurt on T1 Eldar.
CL has his underslung flamer upgrade, which bleeds Eldar like no tomorrow. He's a moving tank that hardly cares about DA damage and often requires shees or a shuriken to drive off. Provided banshees try to close with him he can put up a more than capable fight, even win if his kill the weak is solid. Eldar are often forced to devote quite some units to driving him off and you can use your units to push elsewhere.
PC's default bolter is anathema to Eldar models, plague nades can dissuade shees, or a well placed turret can completely wreck T1 Eldar. Only the immolator blade of the warlock hurts it, but with PC repair support it will live.
In late T1 touch of nurgle becomes available, and it can get most Eldar infantry supermurdered, allowing for a good shot at a crucial engagement.
CS is more difficult, but can ruin Eldar's day by teleporting all over the place, dislodging shurikens or last hitting retreating models, even moreso with sword of flame. Doombolts are a real tool for softening up any Eldar infantry. Raptors or tics with the flame buff are far from easy prey for shees, and if the ladies get whittled down their efficiency drops hard.
I'm not going to write a whole essay on Chaos T1 army comp vs Eldar, Rostam touched on some good points there; what I will add though is add a note on player dependency.
I haven't seen any replay so I only have your description to go off of, but before you get lost on a matchup also consider who you're fighting. Knocking units back with kinetic into a fleeted nade and stuff like that is very high level stuff. Part of your struggles may be up to a significant disparity in experience between yourself with Chaos and your opponent with Eldar.
If you want to discuss things in detail definitely join us on Discord. We have plenty of veterans to discuss strategy and fellow aspirants for practice!