Everybody wants a narrow Kerf line, but It sounds to me like you took too much set out of the saw, especially if it doesn’t have a tapered saw plate.
If you have digital calipers or a micrometer, the set should be around .o6” wider than the thickness of the plate for most wood. A bit more if the wood is wet(.06”-.08”) Dry hardwoods can be a little finer. (04”-.05”)
You can set saws that don’t cut deep, like a dovetail saw, right a the fine end of the scale, but if you are cutting into wood where the whole plate is embeded, you need the wider set. You’ll know if the plate gets warm of if you get chatter on the return stroke that you have way too little set.