It happens because the texture pack you are using isn't compatible with the update. You'll need a post-update version of the texture pack and then do the following:
Cleaning Your Installation
1. Hit Windows Key + R to open the Run console.
2. Type in and enter the following: %appdata%/.minecraft/
To reach the folder on a Mac:
1. Open Finder.
2. Navigate to the following: (Username)/Library/Application Support/minecraft.
3. That should open a folder, in that folder delete the bin folder.
4. Run Minecraft and let it patch. When that's done, close Minecraft completely.
Installing the Texture Pack
1. Save the pack's zip file to the texturepacks folder in your minececraft directory. (Do not extract!)
2.
Click here to download the latest version of MCPatcher.
3. Run MCPatcher, ensure HD Textures, HD Font, CTM, and Custom Colors are ticked then hit Patch, then close it when it's done.
4. Run Minecraft and go to Mods and Texture Packs to select your chosen texture pack.
Simples.