If there was no evidence to back President elect Trump's comment up then it was probably inappropriate. However, it was hi opinion and he has every right to make that comment. I don't see any reason to make a big deal of this. I don't see a reason why people can't investigate the comment.
Americans voted him into office, but that doesn't mean that Trump still doesn't have problems with his temper. He shouldn't be tweeting at the New York Times or anyone else. He should be above things like this. At the same time, he shouldn't be making allegations against illegal voters, because the election is over and he won.
Mr. Trump's comments stem from nothing but hearsay. It is almost like he is back on the playground trying to spread unsubstantiated rumors about the another kid to keep himself in the position of power. The President-Elect is supposed to be someone who is above childish acts like this. If any evidence were available, something like this still would not be acceptable as there are more mature and professional routes that can be taken to address that issue.
If there is no evidence to back it up, then yes, it was in appropriate. However, such should be brought to America’s attention if non-citizens were casting votes and swaying the results when they should not have had the right to vote. No one who is not a valid U.S. citizen should be able to vote. No citizenship, no ballot.