Villa have been bounced out of all three - the FA, League and UEFA Cups - and seen their top four hopes hit by a resurgent Arsenal.
O'Neill said: "I'm responsible for the football club so eventually all the decisions that are made will be mine. It's my responsibility to put a side out to try and win some football games and, of course, I obviously accept all the criticism that's coming round.
"Some of it is a bit over the top but it is less of an issue than you think."
O'Neill added: "You do what you consider is the right thing. You take these decisions. Other sides who have played lesser teams in the League Cup and have gone out have taken less abuse.
"We went as strongly as we could to try and get a lead in the first leg against CSKA Moscow at Villa Park.
"But Aston Villa might not be, for the next 25 years, in with the same chance of qualifying for the Champions League. You never know. I'm not really concerned about it (the abuse). Take the stick, take the punishment. That's my job. I cannot be responsible for what other people write or talk about.
"My time here will be dictated by results and the sort of progress we are hoping to make.
"It's only four weeks ago that Arsene Wenger was told by fans to leave his job and a couple of years ago when Manchester United fans were phoning in saying he (Sir Alex Ferguson) had lost the plot - and they're the champions.
"It's entirely Aston Villa fans' prerogative to do what they want but I'm not so sure that it's entirely helpful at the minute. But it's symptomatic of where we stand here today."