Why does the Laravel API return a 419 status code on POST and PUT methods?

If you are developing REST APIs, its better not add tokens. If you are using 5.4 or 5.5 you can use api.php instead of web.php. In api.php you don’t need token verification on post requests.

If you are using web.php, then you can exclude routes that you don’t want to validate with CSRF Tokens.

Here is the official documentation:

Excluding URIs From CSRF Protection

Sometimes you may wish to exclude a set of URIs from CSRF protection. For example, if you are using Stripe to process payments and are utilizing their webhook system, you will need to exclude your Stripe webhook handler route from CSRF protection since Stripe will not know what CSRF token to send to your routes.

Typically, you should place these kinds of routes outside of the web middleware group that the RouteServiceProvider applies to all routes in the routes/web.php file. However, you may also exclude the routes by adding their URIs to the $except property of the VerifyCsrfToken middleware:

<?php

namespace App\Http\Middleware;

use Illuminate\Foundation\Http\Middleware\VerifyCsrfToken as BaseVerifier;

class VerifyCsrfToken extends BaseVerifier
{
    /**
     * The URIs that should be excluded from CSRF verification.
     *
     * @var array
     */
    protected $except = [
        'stripe/*',
        'http://example.com/foo/bar',
        'http://example.com/foo/*',
    ];
}

For reference https://laravel.com/docs/5.5/csrf