These fabric carrots were made by my mom using strips of orange fabric, styrofoam cones, a hot gun, and fake grass, or whatever you want for the stem part.
Get cones like this, I found different sizes, but you can make different sizes by shaving part of the tops off to make them different lengths. It is messy though so do it in a plastic bag.
Cut a square of fabric and hot glue it down over the top and bottom parts of the carrot, (like in picture below). Glue the edges of the fabric down over the cone part (it will be covered up by the strips of fabric).
Then take orange fabric strips (about 8-10 inches long - ripped about 1 inch wide), and hot glue them on as you work your way down the cone.
Then use scissors or a knife and poke a hole in the top and cut a small circle. Stab your grass or stem part into the cone and hot glue it in.