I guess you did.... I'd use a very fine (3 pixel ) brush to select it. But you have to zoom up close and select an appropriate size with the same diameter of the hairs.
One trick I'd do.... copy the bag on a new layer.... hide the original bag background. ...with the new layer active, play with the brightness controls to bring out as much white in the background. Use the Magic eraser tool set to 15? and delete as much white and grays as you can.
Go to the quick mask mode.... select a fine brush ( 3 pixels ) (why 3 ? you'll know in minute) and zoom in close brush as much hairs as you can without getting X-eyed....lol..... When you're satisfied with the amount of hair you've got from the edges, color the whole bag- straps and all......
When done, exit the mode.... CTRL+SHIFT+I to invert the selection and hit delete.
Now, what's the point we copied the bag? In the event you prefer the original brightness of the original image, simply CTRL+click the layer icon of the cleaned bag to select it. make the background layer active... CTRL+SHIFT+I... and delete the whats around the bag. and if you need a detail from the original bag image that you may have deleted, simply copy the detail on a new layer, use BRIGHTNESS CONTRAST to match the top image and merge....
Now after all that work , I'm sure there's white there most especially around the hairs..... This why I said don't go lower than 3 pixel brush. coz to get rid of the white, you go to MENU>LAYER>DEFRINGE(set to 1 pixel) .... the white, well , at least most of it wil be gone.
Hope this helps you... you gotta be patient with this one..... I've done worse - bags and animals.....