Nixon wanted a recount, but Dwight Eisenhower called him on the carpet and told him to shut up, the country couldn't take the scandal.
Joker in the deck: Ike never liked Nixon and didn't want him in the White House under any circumstances, so his argument was specious at best.
So Nixon knuckled under, and one stolen election, one Johnson dictatorship, and two dead Kennedys and a dead MLK later, a (justifiably) more paranoid Nixon was sworn in anyway.
Conclusion: Nixon should have stood up for himself and fought it out anyway. He was a square shooter in '60, less so in 1969, by which time he was more cynical and surrounded by cynical admen (J. Walter Thompson execs Haldeman and Ehrlichmann, self-promoting pompous hump Henry Kissinger).
This is the first I heard that Nixon was being pressured by Ike and wanted a recount. At any rate, especially if that’s so, he conceded with class and decency. Compare that with Al Gore in 2000 and since, and you can plainly see the difference. May he never hold another public office.