The 2009 world champion could only secure 13th place on the grid ahead of Sunday's Abu Dhabi Grand Prix after early promise in practice failed to rematerialise during the qualifying session.
Button said earlier in the season that any podium before the end of the campaign would have to be considered an achievement as McLaren have had to battle just to be top-10 contenders for much of the year.
There are now just three races left for McLaren to break their 2013 podium duck, but having seen team-mate Sergio Perez drive to a well-deserved fifth place in India and with a general upturn in speed, Button reckons a top-three finish remains a possibility.
"The car felt the best it has all year [before qualifying]," he said.
"There is some good points to be taken by us. A podium is still a long-shot but I think it is more possible after now and India than I probably did for most of the season. It will be nice to end the season on a reasonable high.
"Winning a race is not going to happen but to get some good, consistent results would be good for the team. Most of the weekend I have been happy with the progress and it has been a joy to drive and the car is a lot better to work with.
"I think in the next three races we can still have some good results, this race is made more difficult starting in 13th."
Perez got more from the car and qualified ninth following on from his strong performance last weekend, with the Mexican yet to be confirmed at McLaren for next year.
The former Sauber man is believed to be close to signing a new deal and team principal Martin Whitmarsh has confirmed he expects an announcement soon as he praised Perez's recent form.
When asked about the announcement for McLaren's 2014 driver line-up, Whitmarsh said: "The answer is I suspect we will be making it quite shortly.
"I think Sergio did a great race last week and that is the sort of thing we love to see.
"He was very unlucky today and could have carried through from Q2 in to Q3 and I'm confident that he will do a fantastic job tomorrow.
"Both our race drivers want to beat each other and we want that level of competition, that is how we run our team. The nice thing is we have got two really honest guys."
McLaren currently sit fifth in the constructors championship, although they are almost 200 points behind fourth-placed Lotus, while Button is ninth in the drivers' standings and Perez is three places further back in 12th.