Thanks a lot for this hint. For somebody with the same problem, my solution looks like:

function sewid_simple_events_add_timestamp_field( $post_id ) {
	if ( 'sewid_simple_event' != $_POST['post_type'] ) {
		return;
	}

	$event_date = $_POST['_post_meta']['event_date'][0];

	if ( ! empty( $event_date ) ) {
		$datetime = new DateTime( $event_date );
		update_post_meta( $post_id, 'event_date_timestamp', $datetime->getTimestamp() );
	}

}

add_action( 'save_post', 'sewid_simple_events_add_timestamp_field' );