"I was very nervous and my words just came out wrong," he wrote on Facebook.
The Night Manager star drew censure on social media for a speech in which he referred to aid workers in South Sudan "binge-watching" the programme.
The British actor said that his "only intention" had been "to salute [their] incredible bravery and courage."
"I apologise that my nerves got the better of me," his post continued.
Hiddleston won his first Golden Globe on Sunday - for best performance by an actor in a mini-series or TV movie - for his role in the BBC's adaptation of John le Carre's novel about a hotel manager involved in arms smuggling.
After thanking his co-stars and the show's director, he told "a quick story" about a recent visit to "the youngest country in the world".
"One night... a group of doctors and nurses wanted to say hello... because they had binge-watched The Night Manager," he continued.
"The idea that we could provide some relief and entertainment for the people who... are fixing the world in the places it is broken made me immensely proud."
West Wing star Joshua Malina was among those to take issue with the speech, which drew a mixed response from the Golden Globes audience.
"Thank you to Tom Hiddleston and all actors who dare to perform in projects that are shown in some of the most dangerous parts of the world," he tweeted.
"That was a long story Tom Hiddleston told to pay himself a compliment," wrote the writer and producer Gary Janetti.
Other commentators drew attention to the neutral expressions of actors Naomie Harris and Christian Slater during Hiddleston's address.
Yet his words drew a warmer response from the World Food Programme, who said it felt "honoured" to have been given a mention.
Hiddleston's award was one of three Golden Globes won by The Night Manager, which also picked up supporting actor prizes for Olivia Colman and Hugh Laurie.
Colman, who was not at the Los Angeles ceremony, said she was "gutted" she had not been present to accept "such an enormous honour".
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Actor Tom Hiddleston has apologised for his much-criticised acceptance speech at the Golden Globe awards, admitting it was "inelegantly expressed".