Having taken a point from a 0-0 draw in Sweden on Friday, Ireland have kept themselves in the hunt for 2014 World Cup qualification.
There is, however, little margin for error in Group C and O'Shea acknowledges that there can be no letting up.
Austria are also pushing hard for a runners-up spot and a route into the play-offs, so Ireland know they must go looking for goals on Tuesday.
"There is a good positive atmosphere, but also we're fully aware of the dangers that we face against Austria," O'Shea told Sky Sports News HD.
"The job is only half done. Four points was the target before the two games, and if we can do that after the game on Tuesday then we will be very pleased, but we are not taking Austria lightly.
"We have watched the clips against Germany and Austria caused Germany lots of problems and will be confident from scoring six goals the other night. But we have grown in confidence too, some of our younger players will have grown a lot in confidence from the other night.
"It's a game to look forward to and we will have the home crowd behind us. Hopefully we can get the three points."
Asked if momentum has swung in Ireland's favour on the back of an impressive point in Stockholm, O'Shea added: "Hopefully, if we can beat Austria, it will do.
"I think we have three home games in a row now, so it's really back in our court if we can take advantage of that. The confidence should have grown from the other night and we can look forward to a big game at the Aviva, but also a tough game as well."