Lee didn't have the luxury of time, resources or hindsight that Krick had when he compiled his numbers "using newspaper reports and other sources".
However, from the link you provided:
"The summation provided by Krick raises the total of Confederate dead to about four and a half thousand, and the wounded to roughly twelve and a half thousand, but, of course, this is an incomplete total.Unfortunately, some accounts adopt the total of approximately four and a half thousand rebel deaths and present them as killed in action, thereby suggesting that Confederate losses in killed exceeded Union losses in this category by roughly fifty per cent….the fact that this figure allows for mortally wounded is apparently not understood, or ignored .This is a prime example of the most excellent statistical research being used improperly." (emphasis added)
Given that the US had some 12,000 in their prisoner cages, that makes Mr. Lee's estimate of only 5000 captured or MIA....rather bogus.
To be fair to Mr. Lee, he had a rather bad case of diaria at the time, which accounts to some extent for how badly he led his men.