Mr David Gordon, a trustee of the Tate, was speaking after the Independent revealed how detectives are investigating an elaborate fraud at the London gallery.
Scotland Yard officers, who have made several arrests, are examining claims that the Tate's own archives were altered to authenticate forged works by artists such as Ben Nicholson. The forgeries were then sold.
Mr Gordon, a former chief executive of Independent Television News, said he and fellow trustees - who include Richard, now Lord Attenborough and Bamber Gascoigne - were told of the inquiry two weeks ago.
"The reaction was one of concern that the level of sophistication of art thefts and frauds has got to this point."
But such attacks were very hard to prevent, he said. "There is no such thing as perfect security and when someone has been extremely cunning and determined it is only after the event that you see what you could have done to stop it.
"We want to be accessible to scholars and the public. If someone seeks to take advantage of an institution that is playing a public role then it is very easy for them to do so."
However, Mr Gordon said he was sure that the "highly professional" staff at the Tate would be taking all the appropriate safety measures in the light of the alleged frauds.
Trustees had not been given any names of those allegedly involved and nor had any figure about the potential scale of the fraud been mentioned.
The investigation has continued for six months and other galleries are thought to have been victims of the fraud. Those arrested have been given bail.Reuse content