See https://core.trac.wordpress.org/ticket/58935

admin-action-post-only.php

<?php

namespace PWCC\Nope\CustomAdminPage;

/**
 * Register a custom menu page.
 */
function register_custom_menu_page(){
	add_menu_page(
		__( 'Custom Menu Title', 'custom-admin-page' ),
		'custom menu',
		'manage_options',
		'custompage',
		__NAMESPACE__ . '\\display_custom_menu_page',
		null,
		6
	);
}
add_action( 'admin_menu', __NAMESPACE__ . '\\register_custom_menu_page' );

/**
 * Process a custom action.
 *
 * This action is fired when the form on the custom menu page is submitted.
 * It redirects back to the custom menu page.
 */
function process_custom_action(){
	if( isset( $_POST['page'] ) && $_POST['page'] === 'custompage' ){
		wp_safe_redirect( admin_url( 'admin.php?page=custompage' ) );
	}
}
add_action( 'admin_action_my_custom_admin_action', __NAMESPACE__ . '\\process_custom_action' );

/**
 * Display a custom menu page.
 *
 * This is a simple form that posts data to admin.php without a querystring parameter.
 * It fires the action my_custom_admin_action which redirects back to this form.
 */
function display_custom_menu_page(){
	?>

	<form action="admin.php" method="post">
		On the custom page.
		<input type="hidden" name="page" value="custompage">
		<input type="hidden" name="action" value="my_custom_admin_action">
		<input type="submit" value="Submit">
	</form>

	<?php
}