"He's had his day. He's Pegasus. He's the most incredible battler," she said of Frodon, a Cheltenham specialist, who held off 33-1 outsider Asos and Road To Respect.
"He travelled, my God he jumped, and the moment he got overtaken two out most horses would have quit. He grabbed me by the hands and said don't you dare give up. He's unbelievable!"
Nicholls, who has trained great horses including Kauto Star and Denman, called it "one of the best days ever".
A beaming Frost, who had a fall last year which sidelined her for three months, punched the air after the most high-profile victory by a female rider at the showpiece meeting.
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In an interview with Reuters this month Frost said: "It's The Festival and such a rare thing to win.
"If you look at the top of the mountain, it's a long way up but if you take it step by step then you will keep going up.
"If you only make it half way, well you've still done well and if you get to the top, only then you can take in the view."
Frost was a Festival-winning rider as an amateur in the 2017 Foxhunter Chase on Nicholls-trained Pacha Du Polder.
The Devon-born jockey had chalked up her first Grade One triumph in the Kauto Star Novices' Chase at Kempton in December with Black Corton.
Lizzie Kelly became the first woman to ride a Grade One winner over fences on Tea For Two in the same race in 2015.
Kelly also enjoyed success on Thursday by riding Siruh Du Lac to victory in the Grade Three handicap chase.
Frost had ridden Frodon to three previous wins at Cheltenham on top of victory in the Old Roan Chase at Aintree this season.
(Reporting by Ken Ferris; Editing by Ed Osmond)
