The broadcasting regulator Ofcom criticised the channel after it emerged that it tried to cover up evidence of the racist bullying of contestant Shilpa Shetty in Celebrity Big Brother this year.
At the time, Channel 4 denied that there had been overtly racist behaviour, but unseen footage uncovered in a police investigation proved that the abuse was racially motivated. Duncan has accepted the ruling but has yet to apologise, prompting calls for his resignation.
Caroline Diehl, chief executive of the Media Trust, said the broadcaster had handled the situation badly but defended both Duncan and Channel 4.
"They have a strong record of proactive support and respect for the third sector," she said.