The only solution is adding the video in the description of the post / page or adding the video in the wp_carousel_carousel_text custom field.
But you can modify the WP Carousel's default behaviour to show videos instead of images. You can modify your WP Carousel's theme and replace the image with the content of an specific custom field, for instance, a custom field called "wp_carousel_video".
The array $item has an index called "ID". This index contains the ID of the content in WordPress, so you can use this value to get more information about the content wich is being shown. With $item['ID'] you can get the value of the custom field "wp_carousel_video".
Actually you can modify WP Carousel to do everything that you want with its API for themes and extras, you only must be creative and take a look at the
documentation.