When I first saw the above tweet from our president-select, I thought what you thought: Jeez. This guy has so many ego problems, he can't even be satisfied to win the Presidency of the United States. It's bugging the hell out of him that Hillary got two million more votes than he did. His "prize" is tainted.
And that might be what's going on here but maybe it's more like this: Trump deals in "facts" that are so vague, they can't be disproven. That's why so many times, the lie is in the form of "I'm hearing that…" It's a way of getting the fib out there without accepting responsibility for it or having to back it up in any way. In this case, he's assuming that no one can prove there weren't millions of illegal votes…or at least can't prove it so decisively that he and his supporters can't insist it's so.
But maybe he darn well knows there was no significant volume of illegal votes for Hillary Clinton. Maybe it's as simple as this: Trump is going to try to pass certain laws and change certain things about America that, polls and common sense tell us, most Americans do not want to see happen. But if someone objects and points out that a majority of voters didn't want him, he's going to say, "That's a lie. I got more votes than Hillary. America gave me a mandate." It's not a claim so much as a negotiating position, a way of saying "I'm going to do what I want."
Hard to believe that many of those who voted for Trump thought Barack Obama was seizing too much power, ain't it?