You have misunderstood the way targa files work. The transparent background as seen in photoshop would only be displayed in .gif or .png files. In targa format, transparency is saved in a separate alpha channel, as black and white colors.
Go to the channel tab, and if you only see R, B and G channels, click the little "add channel" button at the bottom to create an alpha channel. As above stated, you will there use white for what's visible and black for what's not.
Your texture file will have to be an 8-bit RBG file, and resolution should be 72 pixels (other might work, but i found that it bugs if i use more). Go to Image>Mode to make sure of this.