In all likelihood, you probably aren't doing anything wrong. While cameras are fantastic tools, they aren't magic - thus they don't always get color to match the "existing" color of things. If you post-process your image, you will probably notice that the colors will shift if you begin lower (or raise) the exposure. I notice others (including yourself) mention exposure, so that would be the first place I would start. From the examnples that others have provided, the bird's "red" color is very much a red-orange, as opposed to a red that leans more towards magenta, so the camera's color shift shift is probably not that great. Canon is known for their reds leaning more towards orange, as opposed to Nikon and Sony whose reds usually are more magenta in hue. There are various ways to shift color in post processing, including increasing or decreasing various colors, and also adjusting white balance settings. I think you will find that if one desires a very specific color, then some post processing is often necessary. Usually, for most circumstances, a camera does well enough, but not always.