Thatcher "tough as nails" with a warm side, Colin Powell says

(CBS) Former U.S. Secretary of State Colin Powell remembered Margaret Thatcher as "tough as nails," with a warm side after the former British prime minister's death was announced Monday.

Thatcher, known as "The Iron Lady by both supporters and critics alike, died of a stroke at age 87, her family announced.

Thatcher was "a great leader ... (and) was a determined person," Powell said. "She was someone who had a vision, had a purpose and went after that purpose and she brought everyone along with her for awhile. Of course, she ran into difficulties, as politicians often do. I knew her for 30 years. I watched her on many occasions, and she certainly was, as Gorbachev said, 'The Iron Lady.' We had a lighter view of her. We said, 'Watch out for the handbag.'"

Thatcher "exuded influence and power," Powell said. "The hair style, the dress, her manner, the way in which she carried that handbag -- when she walked into a room, you knew that somebody had arrived and you'd better be careful.

Former U.K. Prime Minister Margaret Thatcher dies at 87

"At the same time, she had an extremely warm side to her, and ... we vacationed with her and (her husband) Dennis once on a cruise, and she could be very, very warm and considerate of other people, as has been reported."

Thatcher was a pivotal figure in an historic time for the U.K.

"She brought United Kingdom back onto solid footing," he said. "The Falklands War was the highlight of her career. She was there at the time Soviet Union was coming to an end. I once came to London after meeting with Gen. Gorbachev ... as national security adviser and I said, 'Well, you know, Madam Prime Minister, Mr. Gorbachev said he'll do as much as he can for as long as he can and then he will just step out of the way if that's appropriate.' She said, 'Oh, young man, even I say things like that.'"

Powell also recalled a time when he was a young major general on the outskirts of political intrigue, watching when Thatcher didn't like the outcome of a competition for a radio contract.

"I was working for Caspar Weinberger, who was our secretary of defense, and there was a competition over a particular radio that we were going to buy from a foreign source, either from the British or the French. It went to the French and Mr. Weinberger had go tell Mrs. Thatcher.

Watch Powell recall this story on "CBS This Morning" in the video below.

"I was with Cap as he walked into that marvelous parlor that the prime minister ... and he started to explain in his lawyerly terms, as only Cap could do, why the contract went to the French," Powell recalled. "And Mrs. Thatcher just looked at him and then said, 'Now, then, Cap, I'm telling you, don't bother trying to explain it to me. It's not explainable. There's been dirty business at the crossroads.'

"Cap took a deep breath and started again and she said, 'Didn't you just hear me, Cap? Don't try to explain it to me.' And then she said something a little untoward about our French allies. Then she looked at me, and waved her finger at me and said, 'Don't write that down, young man.'"

For more with Powell and his memories of Thatcher -- including her political life as it related to the U.S. and Presidents Ronald Reagan and George H.W. Bush -- watch the video above.