A drop in blood glucose (sugar) level is fairly common after giving blood, leading to the symptoms described by both yourself and DONNA1458. A high sugar/energy drink after giving blood should rectify the problem. If you drink the night before giving blood, it might be worth cutting back or avoiding all together. The dehydration resulting the next day and the potential drop in blood sugars is not a good combination.
Another possibility is the time of the day. Try donating later in the day if possible. (there is logic there but I don't want to bore you with the rationale!)
Finally, it is unlikely to be something underlying such as anaemia, as this should be ruled out in the pre-donation check.
Try a energy before and/or after donation.