Sir Ian Cheshire, chair of the charity, told the BBC that the "optics" of accepting so much cash did not look good, but that at the time it was not uncommon for wealthy people in the Middle Eastern to use large amounts of cash.
He said that more recent money-laundering regulations would make it unlikely that large amounts of cash would now be offered or accepted.
It was one of three lots of cash, totalling €3 million, which Prince Charles personally received from Sheikh Hamad bin Jassim bin Jaber Al Thani, the former prime minister of Qatar, between 2011 and 2015.
On one occasion, Sheikh Hamad presented the prince with €1 million, which was reportedly stuffed into carrier bags from Fortnum & Mason, the luxury department store that has a royal charter to provide the prince's groceries and tea.
On another, Charles accepted a holdall containing €1 million during a private one-on-one meeting at Clarence House in 2015.