Mrs Cooper, who saw her majority in Normanton, Pontefract and Castleford slashed from 14,499 to 1,762 at last week's General Election as she lost more than 10,000 votes compared with 2017, said Labour had to change after its worst performance since 1935.
She confirmed she was considering running to be Labour leader to replace Jeremy Corbyn, who last night faced fury from his own MPs and was accused of being a "preening narcissist" by Mary Creagh, who lost her Wakefield seat to the Conservatives.
Mrs Cooper, who was Chief Secretary to the Treasury under Gordon Brown, told BBC Radio 4's Today programme that there were "a lot of things to reflect on" for Labour.
She added: "I think we do clearly have to change because it hasn't worked and we've got the fewest Labour MPs since 1935 and a big drop in working class support with low income voters choosing the Conservatives even though they didn't want to and felt let down by the choice that we gave them, so we have to show some humility because we got things wrong."
Ms Cooper said both Mr Corbyn and former Prime Minister Tony Blair, who today makes a speech calling for Labour to change its direction, are "seen as internationalist, not patriots, and we should be able to be both patriotic and outward-looking because that's what we were in 1945".
She added: "There are three things we are going to have to do now, and one of those is about recognising that we cannot become a party that is concentrated in cities, with our support increasingly concentrated in diverse young, fast-moving areas, while older voters in towns think we aren't listening to them.
"That is not a left-right issue, because both the left and the right of out party are seen as internationalist, not patriotic. That might not be fair but it is how we are seen. We should be able to be both patriotic and outward-looking, that is what we were in 1945."
Asked if she would consider running for leader, she said: "The contest doesn't start until January. I will decide over Christmas what I am going to do, we have just had a hard local campaign. I have stood before but the party membership has changed a lot.
"I am going to reflect over Christmas, the issue is what kind of party we have now as well as what kind of party we need to become. And that is for all of us to think about, what role we want to play in it."
Mr Corbyn was this week confronted and called a "preening narcissist" by a former Labour MP who lost her seat in the election.
Mary Creagh was angry after she lost her job as the MP for Wakefield last week when her 2,000 majority was overturned by Conservative Imran Ahman Khan.
The 52-year-old told Channel 4 News that she spoke to Mr Corbyn in Westminster on Tuesday as she returned to clear her office and speak to former staff.
She blamed him for "enabling a hard Brexit" and "five years of austerity," adding: "This was Jeremy's manifesto, Jeremy as the leader, Jeremy's NEC, Jeremy's plan, called at Jeremy's time."
She said "on the doorsteps there were two words" used to describe the leader's approach, but that she could not repeat them "pre-watershed".
Ms Creagh also told the programme that no senior Labour figures had been in touch since last week's vote, adding: "I've had no phone calls or messages from anyone in Jeremy or his team.
"Given I was in today, telling my staff that they're going to be redundant a week before Christmas, shows in Jeremy we have a man without honour and without shame - and a type of preening narcissism that means he thinks he's still got something left to offer our Labour movement."
Ms Creagh's comments came as the Parliamentary Labour Party (PLP) met for the first time since the party's biggest defeat in more than 80 years.
At the meeting, Jess Phillips said that other colleagues who had lost their seats had not heard from party bosses.
Leaving the meeting, the Birmingham Yardley MP said she read out a text from Melanie Onn, who lost her Great Grimsby seat to the Tories, about "how she had been let down by the leadership and the frontbench and that nobody had bothered with Grimsby.
Former shadow work and pensions shadow Rachel Reeves said she told the meeting Labour needs "radical change" and get a leader "that actually wants to win".
"If we want to change the lives of the people we came into politics to serve then we've got to win power and that's not been possible two times under Jeremy Corbyn's leadership," Ms Reeves told reporters.