As others have said above, the camera's meter is likely to be trying to interpret the white background as mid-grey and shift everything accordingly. So you end up with an underexposed image. It isn't an unusual situation and people often experience it when taking photos with bright backgrounds, like winter (snow) scenes.
You can try to correct in camera or in post, but getting as close as possible in camera is likely to give you the most flexibility in post. So, two options that spring to mind are:
1) Switch your metering to spot (or another narrow mode) and meter off the flower. This is likely to work but runs the risk of blowing your highlights in some cases.
2) With above or on it's own: knowing that you have quite a large area of white, use manual or exposure compensation to push the whites to where they should be. Use your camera's histogram to check the results to avoid over exposure. In your case you should have a bunch of vertical lines towards the right of the histogram (in the highlight area). Just be careful to have a small gap between the righthand end of the histogram and your data on the graph to avoid overexposing (if you are using RAW you'll have a bit of latitude anyway because most cameras that I'm aware of use the jpeg data for the histogram, not the raw data).