Give Viper's Video Quicktags a look, it makes embedding video a snap. It also includes ways to size up the video really easily.
It's what I used before going with just embeds.
I agree with Jan. You should go with a plugin like Vipers Video Quicktags. If it does not work out for you, search Google for plugins for your problem. You most probably will get a good plugin.
JetPack does handle that shortcode, so if you have that plugin installed and the feature activated then you should be good to go.
Also, Jetpack is great. Click on the Jetpack link for more info about it. Set up a WordPress.com account to make it work. Jetpack usually comes installed already with WordPress.
Also, could you post the link of your site where the video is. We might be able to help you out more with the link.