One more thing to use Single File Component (.vue file), css-loader.
Here is a quick way to add css-laoder to webpack config.

Install packages

yarn add css-loader node-sass sass-loader mini-css-extract-plugin -D

webpack config

In your webpack.config, add modules rules like

module.exports = {
    ...
    module: {
        rules: [
            {
                test: /\.scss$/,
                use: [
                    MiniCssExtractPlugin.loader,
                    'css-loader',
                    'sass-loader'
                ]
            },
        ],
    }
    ...
}

In your webpack.config, add plugins like

var MiniCssExtractPlugin = require('mini-css-extract-plugin')
module.exports = {
    ...
    plugins: [
        new VueLoaderPlugin(),
        new MiniCssExtractPlugin({
            filename: 'components.css'
        })
    ]
    ...
}

In your html, load css.

<link rel="stylesheet" href="/assets/components.css">

I am using jekyll-assets to these files to be digested.

Recources

vue-loader
https://github.com/sumiki/sumiki.github.io.src