Meeting the first minister on a visit to Cardiff, she said she wanted Welsh Labour and the UK party to work more closely together.
Ms Cooper said "much more frequent, strong, regular" shadow cabinet meetings in Wales were also needed.
She said the party should learn from the "great job" Welsh Labour was doing.
Ms Cooper, the shadow home secretary, told BBC Wales: "I think we've got to strengthen that relationship, I think it's really important.
"We only had on one occasion a Labour shadow cabinet meeting in Wales with the Welsh leadership.
"We need to have much more frequent, strong meetings, regular arrangements in terms of the shadow cabinet coming to Wales for meetings, and also the Welsh leadership coming and being a part of shadow cabinet meetings in Westminster as well."
Ms Cooper added that she wanted to see a change in the way Wales is funded before income tax powers are devolved.
"I think you've got to have fair funding," she said.
"There have been all sorts of historic problems for Wales as part of the Barnett Formula.
"It's important for Scotland but the way it works for Wales does, I think, need to be changed to ensure you've got that fair funding.
"In the end I think it's right it should be up for the people of Wales to decide in terms of income tax.
"But that fair funding is the bottom line."
Ms Cooper is up against Jeremy Corbyn, Andy Burnham and Liz Kendall in the race to succeed Ed Miliband as Labour leader.
The winner will be announced before the party's annual conference in September.
Labour leadership candidate Yvette Cooper has said Carwyn Jones should attend shadow cabinet meetings at Westminster to boost its Welsh links.