But in a small show of defiance, she did refuse to smile.
In her new book Becoming, Ms Obama reveals what she was thinking as her husband Barack handed over the world's most powerful job to Mr Trump.
The new President's first act was to deliver an inauguration speech unlike any that had come before, in which he painted a dark image of "American carnage".
"Someone from Barack's administration might have said that the optics there were bad, that what the public saw didn't reflect the President's reality or ideals. But in this case, maybe it did," Ms Obama writes, according to ABC News.
"Realising it, I made my own optic adjustment. I stopped even trying to smile."
Ms Obama was interviewed on Good Morning America as part of the publicity drive for her book, which due to be released tonight.
She was wary of openly criticising Mr Trump on camera, but did take a backhanded swipe at his capacity to do the job. There were also hints of frustration at his election victory.
"Being the commander-in-chief is a hard job, and you need to have discipline, and you need to read, you need to be knowledgeable, you have to know history, you have to be careful with your words," she told reporter Robin Roberts.
"But voters make those decisions. And once the voters have spoken, we live with what we live with."
Ms Obama spoke frankly about the toll politics had taken on her.
"I don't think we do each other a service by pretending hurtful things don't hurt," she said.
"That's what I've come to. I need to own that hurt, to talk about it. I need to process it for myself so I can heal. But at the time, I wasn't going to allow myself to feel victimised. There was no time to hurt in that role."
From left, First Lady Melania Trump, President Donald Trump, former President Barack Obama, and former First Lady Michelle Obama talk on the steps of the U.S. Capitol. Photo / Getty Images
In her book, Ms Obama isn't quite so careful to avoid direct criticism of the President.
She reportedly writes that she will "never forgive" Mr Trump for feeding the racist "birther" conspiracy theory that Mr Obama was actually born in Kenya, and therefore ineligible to be president.
U.S. first lady Michelle Obama (R) greets President-elect Donald Trump as (L-R) Melania Trump, Tiffany Trump and Ivanka Trump look on, on the West Front of the U.S. Capitol. Photo / Getty Images
"She got paid a lot of money to write a book, and they always insist that you come up with controversy," he told reporters.
"I'll give you a little controversy back. I'll never forgive (Mr Obama) for what he did to our US military. It was depleted, and I had to fix it."
This is an unusual situation. It is rare for a former president — or indeed a former first lady — to speak out publicly against the White House's current occupants.
But Mr Obama was a conspicuous presence in the lead-up to last week's critical midterm elections. He campaigned relentlessly on behalf of Mr Trump's political opponents, the Democrats.
"What we have not seen, at least in my memory, is where right now you've got politicians blatantly, repeatedly, baldly, shamelessly lying. Just making stuff up," he told voters.
Mr Obama mocked Mr Trump's record, implying there was corruption in his administration.
"They promised to take on corruption. Instead, they have racked up enough indictments to field a football team," he said.
"I didn't have anyone in my administration get indicted. I just thought that was how you were supposed to do things."
Ms Obama looked visibly unimpressed. Photo / Getty Images
He also ridiculed the President's focus on a caravan of migrants heading towards the Mexican border.
"They are telling us that the single greatest threat to America is a bunch of poor, impoverished, broken, hungry refugees 1000 miles away," Mr Obama said at one rally, his voice rising incredulously.
Mr Trump repeatedly hammered the caravan during his own campaign appearances, and insisted it was hiding "criminals and unknown Middle Easterners".
Everybody knew who Mr Obama was talking about, but he nevertheless avoided mentioning Mr Trump by name, in a small but significant acknowledgement of the fact that presidents don't normally attack each other.
"I think Obama feels that Trump is taking America in a dramatically wrong direction as a country," Professor Brendon O'Connor from the US Studies Centre told news.com.au at the time.
"His foreign policy, and this lack of civility that Trump represents — I think he sees speaking out as exceptional behaviour required by exceptional circumstances."
Ms Obama is clearly dealing with the same problem.
