"The foreign policy mistakes of the post-war period are my honest views".
Bercow, who was persistently accused of bias by Brexit-backing MPs during his term as Speaker, gave a valedictory speech to the Foreign Press Association, revealing himself to be a remainder.
He added: "I don't think it helps the UK".
Hoyle was elected speaker of Britain's House of Commons on Monday, chosen by lawmakers from among seven candidates to replace the influential but contentious Bercow.
Mr Bercow - who was a Conservative MP before being elected to the Speaker role in 2009 - was often sharply criticised by members of his former party for his decisions regarding Brexit debates in the Commons.
"I respect the prime minister and he has the right to do what he did also in the House of Commons".
Broadcaster Piers Morgan, who voted Remain in the 2016 European Union referendum, said: "Astonishing admission that will confirm every suspicion Bercow did all he could as supposedly impartial Speaker to stop Brexit happening".
I genuinely believe Sir Lindsay Hoyle has it in him to become one of the greatest Speakers we have ever had. "The honest answer is no, I don't", he said.
Bercow later told NHK it is a challenge for Parliament, for the government and for the country to reach a conclusion on Brexit, and there is no guarantee they will do so soon.
Sir Lindsay's election was greeted with a flurry of tributes from MPs on his first full day as Speaker.
Foreign Secretary Dominic Raab told the Speaker: "You will not have an easy task but I'm confident that with your technical expertise, your long experience and good humour, you'll do an absolutely superb job".
Sir Lindsay, formerly a deputy to Mr Bercow, received 325 votes to Mr Bryant's 213.