His comments came as electoral college electors put Joe Biden, president-elect, over the 270 vote threshold needed to enter the White House come January next year.
Mr Biden’s victory has been accepted for weeks, but last night’s meeting of the EC cements his win, all but ending the outgoing president’s desperate bid to hang onto power.
Some congressional Republicans, who have for weeks refused to acknowledge Mr Biden as president, are now accepting the election is over.
“It’s time for everybody to move on,” said John Thune of South Dakota, the No 2 Senate Republican. Mr Trump’s legal effort to overturn the result is “not going anywhere,” he added.
The defeated incumbent, however, continues to insist, without evidence, that the election was “stolen” from him, claims supported by a substantial number of House Republicans.
Speaking to CNN as Mr Biden’s win was officially recognised, Mr Hogan said the president and his supporters are “running out of road” in their bid to overturn the election result.
Mr Hogan said he accepted that the president had the legal right to challenge the results in key battleground states.
But since his legal team has failed to produce any credible evidence of widespread voter fraud, “we just have to acknowledge” Mr Biden won the election, said Mr Hogan.
Refusing to do so is “embarrassing us”, the Republican governor said. “It’s an affront to our democratic process and it’s diminishing the presidency.”
He added: “I think it’s bad for our party, bad for the country, and it weakens our position in the world.”
Despite the pleas of Mr Hogan and other GOP figures, Mr Trump is showing no signs of giving up his attempts to overturn an election he lost by 74 Electoral College votes – an exact reversal of his 2016 win, which he claimed was a landslide.
He is ploughing ahead despite suffering a host of legal defeats aimed at overturning the results in a handful of key battleground states.
Last week, the Supreme Court threw out a lawsuit filed by Trump’s legal team in Texas, which asked election officials there not to recognise Mr Biden’s wins in Michigan, Pennsylvania, Georgia and Wisconsin.
And the president’s stranglehold on the Republican Party is underlined by the fact that 120 House Republicans – nearly two-thirds of the party’s seats in the lower chamber – supported that legal challenge.
Multiple figures from across the political spectrum have suggested those politicians continuing to support the president are only doing so out of fear.
In a year for record turnout, Mr Trump secured some 75 million votes at the election, more than any other defeated presidential candidate in history.
Many of those votes helped GOP House incumbents and candidates to hold or win their seats. This, Capitol Hill observers say, is why they refuse to publicly criticise the president or denounce his false voter fraud claims.
Mr Trump is all too aware of the influence he has over those politicians and last night reminded them of it.
“Get moving Republicans,” he tweeted in response to a report which claimed that there had been ballot irregularities in Michigan.
“75 MILLION VOTES”, he added with emphasis as he called on politicians to frustrate the democratic process in the Rust Belt state and other key swing states.
Meanwhile, Mr Biden continues to prepare for government and last night said it was “time to turn the page” in remarks delivered after the EC confirmed his win.
“Respecting the will of the people is at the heart of our democracy, even when we find those results hard to accept,” he said in remarks delivered from Delaware.
“The flame of democracy was lit in this nation a long time ago. And we know that nothing not even a pandemic or an abuse of power can extinguish that flame.”