The Queen's horse Carlton House may have won the 2011 Derby if the race had been run differently, her team said.
French raider Pour Moi won the Classic on Saturday from Irish challenger Treasure Beach in a tight finish, with the Royal colt closely behind in third.
Carlton House's jockey Ryan Moore indicated his mount was unlucky, said the Queen's racing manager John Warren.
"Ryan felt if the circumstances had been different so would the result," said Warren.
Carlton House, sent off 5-2 favourite, was drawn widest of all in stall 13 and the three-time champion jockey had a tricky task to get him to the front.
And Moore's task was not made any easier when Carlton House lost a shoe in the final furlong as he tried to gain ground.
The Dante Stakes winner closed on leader Treasure Beach but finished three-quarters of a length behind the runner-up, with Pour Moi coming from last to first to win by a head in the final strides.
"Ryan is disappointed but said it was a messy race and the horse slightly missed the kick," said Warren.
"He said a few horses, the long outsiders, came back on him and that didn't help him get into the smooth rhythm that he wanted.
"As a consequence he had to make his run from further back than he wanted. He felt if the circumstances had been different so would the result.
"I would say it was just the run of the race that did us no favours. If he takes on the same horses again, who knows, the result might be different."
The defeat means the Queen's best finish in a Derby remains the second for Aureole in the 1953 running during her Coronation year.
Carlton House's preparations for the big race were hampered when he suffered a minor ankle strain.
Trainer Sir Michael Stoute, who has won the Derby five times, said: "He's run very well but things just haven't gone right."
Mickael Barzalona had to come from even further back as he guided the winner Pour Moi, a 4-1 second favourite, to a dramatic victory.
The 19-year-old celebrated by standing in his riding irons as he crossed the winning line after triumphing in in his first Derby ride.
"It is fabulous. It is brilliant and I came so fast at the end that I knew I was going to win," said the French teenager.
It was a first Epsom Derby win for Andre Fabre, who was saddling the first French-trained winner since Empery in 1976.
Asked about the Queen, the 22-times champion French trainer said: "It is a race between horses, not between persons, otherwise I would have finished far behind Her Majesty."
The winner is owned by the Coolmore Stud trio of John Magnier, Michael Tabor and Derrick Smith, who are also involved in the ownership of runner-up Treasure Beach, trained in Ireland by Aidan O'Brien.