It is apparently very common for people who do strength training using lifting straps, to have wrist pain if not done properly. The wrist is not designed to carry your body weight. The tendons in your wrist and within your carpal tunnel can become inflamed causing tenderness and pain. I experienced this for 2 days and had a significant loss of hand strength. Thankfully with rest this has subsided.
In the future I will continue to try to strengthen my grip strength naturally and only use lifting straps on my last set, when my grip gives out. As well, the lifting straps should be placed not at the wrist but below the ulnar head, the bulbous bone on the outside of your wrist, closer to your body, by about 1″. This should allow the strap to pull from your radius-ulna and not your carpal tunnel area.
There are other cautionary notes about using lifting straps. While these straps are simple devices, there is more to them than meets the eye.