Key workers have been "overlooked and underpaid" and there will have to be a "reckoning" after the coronavirus crisis, the new Labour leader has said.
Sir Keir Starmer told the BBC's Andrew Marr: "They were last and now they've got to be first."
He said another decade of austerity would be a mistake, saying it was "inevitable" that the wealthy would have to pay more.
The 57-year-old won the contest to succeed Jeremy Corbyn on Saturday.
He defeated Lisa Nandy and Rebecca Long-Bailey in a ballot of party members and other supporters.
Meanwhile, Sir Keir has announced some members of his new shadow cabinet, including former leadership rival Lisa Nandy as shadow foreign secretary.
Speaking to the BBC's Andrew Marr Show, Sir Keir said: "What we can't do is go back to business as usual we now know who the key workers are, they have very often been overlooked, underpaid and there has got to be a change."
He said funding of the NHS had to be looked at and "we have to think about how we reimagine the economy going forward".
"I think it is inevitable that we have to ask those that have more to pay more," he said.
"When we are through [the coronavirus crisis] there is going to have to be a reckoning, we are going to have to do things differently."
His comments come as Health Secretary Matt Hancock has warned that exercise outside the home could be banned if people ignore the lockdown rules on staying at home and social distance.
Sir Keir said Labour would support the government if it decides to take the step of further restrictions, including on exercising outside the home.
He was it was "particularly difficult" for those who do not have gardens or live in overcrowded homes, but he said: "We have got to get through this. Every time people break the guidance from the government, they put other people at risk".
But, he said, the government had to plan an exit strategy to end the lockdown, including a national vaccination programme, and this should be published.
Sir Keir said that "as soon as" a vaccine arrives, there had to be a plan to roll it out nationally, "but priority obviously for those on the front line".
Asked about the deadline for a post-Brexit UK-EU trade deal and whether the government can meet it, Sir Keir said the December 2020 deadline was "unlikely" but, he said, the focus had to be on dealing with the coronavirus outbreak.
He added that the "very, very tight" deadline should be extended "if necessary".
Sir Keir also said he spent time after the leadership election result "reaching out" to members of the Jewish community, after he apologised for the "stain" of anti-Semitism that has tainted Labour in recent years.
He said his success will be judged on whether Jewish members return to Labour.
Elsewhere, writing in an article in the Sunday Times, Sir Keir said failure to provide enough protective equipment for frontline workers and delays over testing had been "serious mistakes" in tackling coronavirus.
He said that ministers took too long to explain why they were "so far behind" on testing.
With the government having promised it will dramatically increase coronavirus testing to 100,000 a day by the end of the month, Sir Keir said its "greater clarity" over testing "should have come sooner".
"Now the focus must be on making sure the promise of 100,000 tests is delivered and that these tests reach those who need them most, including our frontline NHS staff," he added.
Labour confirmed that Sir Keir had been briefed on the coronavirus outbreak by senior government officials.
"During the call, the Labour leader reiterated his commitment to work constructively with the government in the national interest," a spokesman said.
Sir Keir, who became an MP in 2015, won the Labour leadership contest on the first round of voting, with more than 50% of ballots cast.
Meanwhile, shadow education secretary Angela Rayner was elected deputy leader, replacing Tom Watson, who stood down as an MP before the election.