The Irish duo finished eighth in the annual song contest with their entry 'Lipstick'. Their energetic performance saw them finish higher than UK representatives Blue.
"We were really proud of ourselves. We did X Factor and all our fans saw us on that. Eurovision is a huge launch pad and now we have loads of support in Europe," Edward Grimes told Star magazine.
His brother John continued: "Well we came eighth, but we are the people everyone is talking about. We wanted to make a huge impact in Europe and I think we did that. Everyone in the world has heard of Jedward now."
Asked if they would consider taking part in the competition again, the twins said: "We would love to do it again. It would be like Jedward: The Return."
On their manager Louis Walsh's reaction to their performance, John added: "He said there's so much more to come for us. He got texts from people, like Simon Cowell and even Bono from U2, saying well done to us!"
Jedward performed for US President Barack Obama in Ireland yesterday as he began a European trip in Dublin.
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Watch Jedward perform 'Lipstick' below: