Ghana were beaten by a stoppage time goal by the Cape Verde Islands, the smallest of the 24 teams at the tournament in the Ivory Coast in one of several shock results on Sunday.
Hughton was accosted at the team hotel as Ghana returned from the match but the angry fan was intercepted by security officials.
Hughton was also subjected to a volley of verbal abuse, the Ghana team media liaison Henry Asante told Reuters.
"The fan approached the coach to express his disappointment at the outcome of the game and told the coach to improve or leave the job," Asante said.
"It was a verbal confrontation. There was no physical contact. Later he was taken away by the security."
It was a second successive defeat by an underrated opponent after Ghana lost in November in the World Cup qualifiers to Comoros.
"We are incredibly, hugely disappointed with the result. We came into the game with a game plan," Hughton told a press conference.
"We changed the way of playing, the system a bit so that we could start on the front foot.
"We thought the team that were put out was certainly a more offensive team. This was our intention.
"I think it rocked us the (first) goal that we conceded but I thought we got back into the game."
Ghana were behind after 17 minutes in a match in which they were highly fancied and fielded a team full of players based at European clubs.
They equalised in the second half but were beaten by a stoppage-time strike from Garry Rodrigues.
"At that stage (when Ghana equalised) it looked like we could go on and win it. We are hugely, hugely disappointed with our result," Hughton said.
"And I know, and this group of players also know, how the Ghanaian people see this game, see this tournament and our expectations going into this one."
Former Ireland international Hughton, whose father hailed from Ghana, has been coach of the team since March, having helped them at the 2022 World Cup finals in Qatar as a technical advisor.
His record is four wins in 11 games.
