There are a few ways to remove pet hair from your carpet without using a vacuum. One way is to use a lint roller. This will work best if your carpet is not too hairy. Another way is to use tape. Put some tape on your hand and then run it over the hairy areas of your carpet. The hair will stick to the tape and you can then remove it. Finally, you can try using a damp cloth. Wet the cloth and then rub it over the hairy areas of your carpet. The hair should come up with the cloth.