The former prime minister said the party was in danger of “slipping back” and it will only thrive if it is “a party of the future”.
In an interview with the Evening Standard, Mr Cameron appeared to suggest the Tories had become complacent after election victories in 2010 and 2015.
Speaking to the newspaper – which is run by his former chancellor George Osborne – Mr Cameron said: “It is very important that the Conservative Party doesn’t slip backwards.
“The Conservative Party only succeeds if it is a party of the future.
“Modernisation isn’t an event. It is a process. A political party should be asking itself all the time, ‘Am I properly in touch with and reflecting the society and the country?’.
“I want us to go on being the open, liberal, tolerant party that we became post-2005 because I think that was part of our success.”
Mr Cameron said a more positive vision was required to fight back against Labour leader Jeremy Corbyn, who enthused thousands of young voters in the campaign.
“We on the centre-right side of the argument have to have just as inspiring a vision – a more inspiring vision – of how you build not just a strong economy but a strong society and a better life,” he said.
Mr Cameron claimed a number of the Labour leader’s young supporters had “forgotten just how dangerous this full-on programme of nationalisation, state control and rampantly high taxes can be”.
He added: “You don’t win the argument in favour of free enterprise, free markets, choice and liberal democracy and then pack up and go home.
“You have to win the argument in every generation.”
Mr Cameron also joked that he would like to strap some of his former cabinet ministers on a raft and send them down a “very, very dangerous river”.
Asked whether any of his former colleagues could benefit from the kind of outdoors courses provided by the National Citizen Service scheme he founded, Mr Cameron said: “If it involved crossing a very, very dangerous river on a raft, I can think of a few I’d want to strap together.”
Mr Cameron also revealed he is halfway through writing his memoirs about his time in Downing Street, adding he was enjoying the process even though it was “hard work”.
The former PM promised the eagerly awaited tome would be a “rip-roaring read”.