"An internal mistake" led Lego to deny a bulk order from Chinese dissident artist Ai Weiwei last year, the company said.
The artist wanted the toy bricks for an exhibition in Australia.
Former chief executive Kjeld Kirk Kristiansen admitted the mistake, while his son Thomas told the Wall Street Journal it was "a typical example of what can go wrong in a big company".
After Lego initially refused the order, citing a policy of not donating for public projects, people in various countries began to donate bricks.
In January, the company announced a new policy, saying it would no longer ask what the purpose of a public project was but would ask customers to make clear Lego does not support or endorse them.
The admission came as Lego announced plans to reshuffle its top leadership to create a "smooth handover of active ownership to the next generation".
Mr Kristiansen, the company founder's grandson, said he will leave his position as deputy chairman to 37-year-old Thomas. The 68-year-old father will take a seat on the board.
He said the aim was "to maintain active family ownership of the Lego Group".
After 25 years as chief executive, Mr Kristiansen was replaced in 2004 by Joergen Vig Knudstorp, an outsider to the founding family who helped bring Lego A/S from a loss to a profit.
Known for its assortment of building blocks, Lego is not publicly listed and does not release quarterly figures.
However, the group, based in Billund, western Denmark, has published earnings reports since 1997.
Last year, net profit was up more than 30% from 2014, at 9.2 billion kroner (£960 million), while revenue grew 25% to 35.8 billion kroner (£3.7 billion).
The number of employees also grew by more than 15% in 2015 to 17,300.
The company was launched in 1932 and the first snap-together Lego bricks were created in 1949.
Mr Kristiansen is considered Denmark's richest man and is worth 9.7 billion US dollars (£6.6 billion), according to Forbes magazine.