She added that she hoped the next Professor of Poetry would be a woman.
An Oxford University spokeswoman said they "respected" Padel's decision.
"This has been a difficult chapter for all concerned and a period of reflection may now be in order," she said.
Walcott pulled out of the contest after Oxford academics received more than 100 anonymous letters reportedly detailing an allegation of sexual harassment made against him in 1982.
He described it as a "low and degrading" campaign.
Padel said: "As a result of student concern, I naively - and with hindsight unwisely - passed on to two journalists, whom I believed to be covering the whole election responsibly, information that was already in the public domain."
It's deeply, deeply disappointing that things worked out this way
Prof AC Grayling Birkbeck College
She added: "I acted in complete good faith, and would have been happy to lose to Derek, but I can see that people might interpret my actions otherwise.
"I wish to do what is best for the university and I understand that opinion there is divided. I therefore resign from the Chair of Poetry. I hope wounds will now heal and I wish the next professor all the best."
Padel was elected with 297 votes cast by Oxford graduates and academic staff, making her the first woman to take up the role since its creation in 1708.
One of those who had nominated her, AC Grayling, the Professor of Philosophy at Birkbeck College, told BBC Radio 4's The World Tonight she was right to step down.
"It would have been really marvellous actually to have a women professor of poetry at Oxford, had it been a straightforward, clean fight.
"So it's deeply, deeply disappointing that things worked out this way and that this kind of scurrilous...campaign was run against Derek Walcott."
Poet Michael Horowitz describes how media manipulation has infected the world of poetry
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.