The candidate gave a speech while on a visit to Leeds on Saturday, supported by the Leeds North East MP Fabian Hamilton.
Ms Thornberry is running alongside Keir Starmer, Lisa Nandy and Rebecca Long-Bailey to take over from Jeremy Corbyn later this year.
She said she was "applying for the hardest job in the country" and hoped to unite the party following a disastrous result in last month's election.
Winning back the trust of voters in 'red wall' areas which had turned blue and addressing the party's problem with sectarianism and antisemitism were high on her agenda.
However, Ms Thornberry criticised the right wing media's treatment of Mr Corbyn, suggesting it had been integral to his lack of popularity among voters.
"We need to have a leader that knows that she has a certain amount of political capital", she said, addressing party members at Leeds Civic Hall.
"They need to sort out the antisemitism problem. We need to work in conjunction with each other. We need to lead from the front and not be sectarian."
Ms Thornberry was due to attend a hustings at the Royal Armouries in the city on Saturday alongside other leadership candidates, although this had to be cancelled due to Keir Starmer suspending his campaign following a family emergency.
A hustings for the deputy leadership, candidates for which include the Leeds East MP Richard Burgon, went ahead as planned.
Ms Thornberry added: "I just think we need to deal with things in a more preferential way and we need to be as hard-nosed as the Tories.
Speaking of Labour's coverage in the media during the election campaign, Ms Thornberry added: "There seemed to have been a change from the real Jeremy that people saw in the 2017 election, and it broke my heart to see such a decent man to have accusations thrown at him that I knew weren't true.
"I think that the leader of the Labour Party has to be the campaigner in chief. You have to do TV, and frankly you have to do it live."
The race to be the next Leader of the Opposition was reduced to four last week after Jess Phillips announced her withdrawal.
Whether a leadership hustings will be re-arranged in Yorkshire is yet to be confirmed.