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Gavin Barwell, who lost his Croydon Central seat but has since taken a key role in Downing Street, said Labour had "tapped into" concerns about the impact of years of public sector pay freezes.
He told a special Panorama programme his party must also do more to listen to Remain voters and their concerns.
The Tories won 42.4% of the vote but Theresa May lost her overall majority.
The party's failure to win outright after Mrs May's decision to call a snap election has led to recriminations and calls for the prime minister - who is seeking to form a minority government with the support of the Democratic Unionist Party - to step down.
The prime minister will address backbench MPs later after reshuffling her cabinet in an attempt to shore up her position - and has won the backing of senior colleagues such as David Davis, Boris Johnson and Amber Rudd.
Mr Barwell lost his marginal seat by more than 5,000 votes as Labour saw its vote increase by 10%. Jeremy Corbyn's party enjoyed a surge in support across the capital, where it picked up a number of seats, although it still ended up with 56 fewer seats across the UK than the Conservatives.
Speaking to Panorama, in a special edition to be broadcast at 20:30 BST, Mr Barwell told the BBC's Nick Robinson that his party must learn the lessons of what had happened.
"There's a conversation I particularly remember with a teacher who had voted for me in 2010 and 2015 and said 'you know I understand the need for a pay freeze for a few years to deal with the deficit but you're now asking for that to go on potentially for 10 or 11 years and that's too much'.
"That is something that Jeremy Corbyn was able to tap into."
On Brexit, he said that there was evidence that "angry" Remain voters had abandoned the Conservatives.
"We are very clear in my seat, that the area of the constituency where Labour did best was the area that had voted heavily for remain… So there's clearly evidence, I think, that people are angry about Brexit still, Jeremy Corbyn somehow managed to get them behind him."
He added: "We do need to make sure that people that are Conservative-minded that voted Remain in the referendum are happy to continue supporting our party."
The interview took place just hours before Mr Barwell was named as the PM's new chief of staff. He has replaced her previous aides Nick Timothy and Fiona Hill who quit in the wake of the election and amid concerns among MPs about the PM's leadership style.
Panorama: Election 2017 - What Next is on BBC1 at 20:30 BST