The Irish were dealt a massive blow to their hopes after only managing to earn a 1-1 draw with Group D rivals Scotland in Dublin on Saturday, but the Ireland captain has set his team a target of getting six points in September.
The Scotland game was seen as a must-win game for the Republic, but the the Los Angeles Galaxy striker is no mood to throw in the towel and has turned his attention to the upcoming trip to Gibraltar and the home clash with Georgia.
The 34-year-old said: “We’ll keep plugging away. We’re definitely not out of this and that was the message that everyone was saying to each other. There’s no way we’re out of this.
“Scotland still have a couple of tough games coming up. There are no easy games in the group, but in our next two games we’ll be looking to get six points.”
The Scots are two points better off than the Irish and now head for Georgia before hosting Germany, and that – on paper at least – looks a significantly harder double-header than the Republic face.
However, Poland, who cemented their place at the top of the table with a 4-0 victory over Georgia in Warsaw, are now five points clear of Ireland with Germany just a point worse off, and with only four games each to play the pair are in pole position to claim the two automatic spots and leave the rest scrambling for a play-off berth.
Asked if he was disappointed with just a point, Keane said: “Yeah, of course. When you dominate the game and everything seems to be going to plan, then we switch off 30 seconds after the start of the second half.
“Football is for 90-plus minutes, so you always have to be switched on, knowing that they have clever players that can do something.
“The goal was a very, very lucky goal but we gave them opportunities to do that. Sometimes you need a bit of luck and they got it.”
Keane was used only as a second-half substitute at the end of a dreadful week for his family, during which his cousins Alan and Stephen Harris died.
The striker revealed he would not have been able to start the game after making just three appearances for his club in recent weeks because of a groin injury, but insisted he was ready to play his part.
He said: “It’s been a tough week. I don’t want to talk about it too much, but for all the family it’s been difficult.
“I was ready for the game. Physically I probably wasn’t ready for it in terms of my fitness and the way I’ve been. I played 90 minutes last week – I was only supposed to play 60 but I ended up playing 90.
“I’ve been out for two months. It’s a long time, so I wouldn’t have been able to start the game, and trying to play for 90 minutes would have been difficult after being out for such a long time.”
Seamus Coleman admitted afterwards the draw felt like a defeat and said the Republic of Ireland must learn from their mistakes if they are to keep alive their hopes of making it to the Euro 2016 finals.
Asked what O’Neill’s reaction had been in the dressing room afterwards, Everton full-back Coleman said: “Like everyone else, he’s disappointed, as you can imagine, any manager’s reaction straight after that.
“We were going to keep it tight and then we concede 45 seconds in, so we got a bit of a slap on the wrist for that, and rightly so.
“As professional players, that shouldn’t be happening 45 seconds into the second half. We have to take that on the chin. You can do all the stuff on the training ground you want, but you can’t really let that happen so early in the second half.”
Coleman added: “To have all your hard work in the first half undone very, very early in the second half is massively disappointing, and it’s hard to take. It feels like a defeat, to be honest.”