The European competition is still the last major trophy Newcastle won when it was the Fairs Cup in 1969.
The Magpies drew 0-0 at home with Metalist Kharkiv in the first leg of the last 32 tie last week and head to Ukraine for the return on Thursday.
And Ameobi feels they can have a good shot at winning the trophy again, saying: "This is a big tournament. It's a European competition, and we want to get as far as we can.
"We're not behind in the tie, which is good. They haven't scored an away goal. The clean sheet's always a nice one to have. We have to go over there and be on the top of our game to win this tie.
"I imagine it'll be quite a hostile atmosphere over there. It's going to be a really difficult game for us.
"You could see they're a really good footballing side - they could open us up.
"We have to make sure we're tight first and foremost, and get an away goal. That could prove decisive for us."