The American city, linked to sportswear firm Nike, was given the event by the IAAF without a bidding process, a decision being investigated in France.
Gothenburg, which missed out, described the process as "bad ethics".
But Eugene said it "adhered to all ethical and legal standards for organizing, presenting and advocating for our bid, according to IAAF rules".
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IAAF president and former vice-president Lord Coe severed his links to Nike after questions over his role in the decision.
But in a statement Eugene said it had submitted identical bids for the 2019 and 2021 World Championships, losing out to Doha in 2019.
It added: "The decision to award the 2021 World Championships to Eugene was made by the IAAF Council in a vote of 23-1."
French officials are already investigating corruption allegations involving former IAAF president Lamine Diack, with Coe quitting the Nike payroll two days after a BBC story suggested he had held talks with Diack and Nike about the awarding of the 2021 event.
Coe, who was reportedly paid £100,000 a year by Nike, said at the time that he "did not lobby anyone" over Eugene's bid, but simply "encouraged them to re-enter another bidding cycle as they had a strong bid".
Gothenburg bid chief Bjorn Erikkson said awarding the World Championships to Eugene had made him "really upset and for very good reasons".
He told BBC World Service: "What happened is bad ethics at least and definitely not professional.
"In the worst of cases it's maybe also criminal, if somebody were there influencing the process, and that's a question that I really want a good answer to."
The former police officer also said he was not sure if Gothenburg would re-enter the bidding process, should it be re-opened.
"It's up to the Gothenburg people, they don't want to answer that question until they know why the last procedure was so unacceptable," he told BBC World Service.
"If you are going to make business with these people you wish to know if they are professional, honest and serious, otherwise maybe you don't want to do business at all."
Coe said that awarding a World Championships without a bidding process "was not without precedence" - the 2007 World Championships in Osaka was one such occasion.
But Erikkson described that as "nonsense".
He added: "If you behave idiotically and unacceptably is it better if you do it twice rather than once? Secondly there are no arguments for doing this, because we who are engaged in the sport wished to have a transparent process, to do it in disguise is not acceptable."
Eugene has defended its role in winning the right to host the 2021 World Championships.