Former US secretary of state Madeleine Albright has warned Donald Trump against American isolationism, telling him after his stunning presidential election victory that national security “cannot be a zero-sum activity” and the US must play its part in the Nato alliance.

“Nato is obviously key. We are responsible for each other, a two-way street,” Albright told the Guardian in an interview on Wednesday.

Trump alarmed many in July when, at the Republican national convention where he accepted his party’s nomination, he implied that the US might not protect other members of Nato if they were not contributing enough to the military costs, and hinted he could withdraw US forces from around the world. A cornerstone of the intergovernmental North Atlantic Treaty Organization’s strength, and global security, is the pact that an attack on one member is an attack on all.

Speaking the morning after the Republican nominee’s shock win and at the moment an emotional Clinton was conceding “painful” defeat for the Democrats and her bid to be America’s first female president, Albright predicted Clinton will never run for the White House again, but hoped another woman soon would.

“There are a lot of women in the system and I hope a woman will run again,” she said.

Albright, who campaigned vigorously for Clinton, also spoke of her fears that Trump would put decades of cultural progress towards greater equality in American society into reverse.

In a dig at his inexperience in public service, Albright said: “It is my hope that once he is better informed he will have a different view … We have to make clear that our national security policy cannot be a zero-sum activity. It has to be win-win and compromises are necessary.”

She warned of the dangers of isolationism, urging the vital importance of deftly managing America’s relationships with Russia and China and adhering to the 2015 multilateral Iran nuclear deal.

“The US must be involved abroad. If we are not engaged, then the system doesn’t work at all, or, even, a new system cannot be created,” she said.

President Bill Clinton appointed Albright as US ambassador to the United Nations in 1993, then as the country’s first female secretary of state in 1997.

When Hillary Clinton was subsequently considering an offer to become secretary of state in Barack Obama’s new administration in 2009, she called Albright for advice.

“I told her she would do a great job. She was a remarkable secretary of state and she would have been a remarkable president, better prepared than anybody, ever,” Albright said.

She declined to predict when the US might now elect its first female president.

Trump ran a notorious campaign during which he denigrated women and bragged of sexual assault, while a string of women accused him of verbally insulting or assailing them.

Albright said: “I am very sad about the way women have been treated during this campaign. That’s brought out some things that are very troubling. And I thought that we had moved beyond that.”

With that and Trump’s innumerable, sustained racist slurs, Albright said the country had gone backwards, culturally, “in some ways”.

“If the campaign rhetoric is an example, there are things that have gone backwards,” she said, without going into further detail.

She predicted a peaceful transfer of power, but wondered obliquely if Trump voters might end up having second thoughts.

“I was in England shortly after Brexit [the vote for Britain to leave the European Union] and the people were very surprised at what they had done,” she said.