The Conservative Party needs to send out a clear sense of purpose and a message of hope if it is to return to power, leading party members have said.
Ms Greening won the Putney seat for the Conservatives
Co-chairman Lord Saatchi said it had to spell out what it stood for, while former frontbencher John Bercow MP said it should send out a "positive vision".
Mr Bercow said it needed to reform itself as well as Labour had.
"We've got to look, to sound and to think more like the country that we want to lead," said the Buckingham MP.
'More work needed'
The Conservatives cut into Labour's huge majority on Thursday, winning back 33 parliamentary seats. But they needed to win 160 to form a government.
Lord Saatchi told BBC News: "The most telling statistic I can put to you is the finding that 70%, a huge majority, of the population, agree with the statement: 'It is hard to know exactly what the Conservatives stand for these days'.
"This is a big problem because, as I see it, in all forms of competitive human activity - whether it is in politics or in business or in war - a clear sense of purpose seems to be the prerequisite for success."
Mountain to climb
And Conservative former foreign secretary Sir Malcolm Rifkind agreed that to connect, the Tories had to inspire both new and old voters with their vision of a "dynamic new Britain".
He told BBC One's The Politics Show: "The Tory party can win the next general election, but by God, it's got a heck of a mountain to climb."
Putney's new Tory MP, Justine Greening, told the show the party had to prove itself an effective opposition, pressing the government on economic stability, if voters were to see it as an alternative government.
All praised the efforts of party leader Michael Howard, who has announced his intention to resign once the party has reviewed its leadership election procedure.
Shadow work and pensions secretary David Willetts said that following the party's third successive defeat, there was a strong mood to recognise its "deep seated problems".
But he told the BBC: "I think we are in a better environment than we have been in the past eight years because Michael Howard, to his enormous credit, has given the party unity and discipline. We now need vision and purpose."
However Labour's communications chief Alastair Campbell said the Tories had "flatlined" and offered another explanation for their regular leadership changes.
"The reason they are in the mess they are in, one of the big reasons, is because Tony (Blair) is such a formidable politician," he told BBC One's Breakfast with Frost.