The LA Galaxy forward has told his Irish colleagues to avoid thinking they are in the finals already as they still have lots of work to do despite sitting on a 4-0 cushion
The LA Galaxy man scored twice in Ireland's 4-0 first-leg victory in Tallinn on Friday - virtually sealing his side's place in Poland and Ukraine next year.
However, there are still 90 minutes of football to be played, and Keane hopes his side do not become complacent.
"In football anything can happen, so we have to do our job properly and professionally. It would be disrespectful to leave the camp now − the job is not done yet," Keane told the press on Monday.
"To lead this group of lads to this stage and hopefully get to the finals would be a great achievement.
"Ireland means a lot to me. I turn up for every game and try my best every time, that's the way I was brought up."
However, despite Keane's upbringing, Estonia midfielder Konstantin Vassiljev hopes to knock down Irish hopes in Dublin by spoiling the party, regardless of whether they qualify for the tournament.
"All of us want to play proper football and achieve a good result in Dublin," said the 27-year-old.
"We need to finish the campaign on a positive note, whether we qualify or not.
"The players and supporters deserve a good performance in the last match of the year and, who knows, maybe a victory too.
"Of course our chances are very small, but if it's possible to concede four goals why can't we score the same amount?
"It's important to score the first goal, and then anything can happen in football."