Speaking at a press conference on Wednesday afternoon, O’Neill said: "After finishing third in a difficult qualifying group, we enter into the play-offs against a very good team in Bosnia and Herzegovina.
"Our fate is in our own hands and we will be doing all that we can to qualify for next summer’s finals.
"We will play the second leg at the Aviva Stadium and that is a big plus for us because the Irish supporters were fantastic in our last game there against Germany and we know that there will be a similar atmosphere for this play-off."
The Republic finished third in their qualifying group, four points behind world champions Germany and three points adrift of second-placed Poland, who beat them 2-1 in the final Group D fixture this month.
Republic of Ireland squad to face Bosnia and Herzegovina: David Forde (Millwall), Shay Given (Stoke City), Keiren Westwood (Sheffield Wednesday), Darren Randolph (West Ham United), Rob Elliot (Newcastle United), Richard Keogh (Derby County), Marc Wilson (Stoke City), Seamus Coleman (Everton), Cyrus Christie (Derby County), John O’Shea (Sunderland), Alex Pearce (Derby County), Shane Duffy (Blackburn Rovers), Ciaran Clark (Aston Villa), Paul McShane (Reading), Stephen Ward (Burnley), Greg Cunningham (Preston North End), Robbie Brady (Norwich City), James McCarthy (Everton), Jeff Hendrick (Derby County), Darron Gibson (Everton), Harry Arter (Bournemouth), Eunan O’Kane (Bournemouth), Glenn Whelan (Stoke City), Paul Green (Rotherham United), Aiden McGeady (Everton), James McClean (West Bromwich Albion), Alan Judge (Brentford), Anthony Pilkington (Cardiff City), David Meyler (Hull City), Jonathan Walters (Stoke City), Wes Hoolahan (Norwich City), Robbie Keane (LA Galaxy), Shane Long (Southampton), Daryl Murphy (Ipswich Town), Kevin Doyle (Colorado Rapids), Anthony Stokes (Celtic), David McGoldrick (Ipswich Town), Adam Rooney (Aberdeen), Simon Cox (Bristol City).