The success of the Commonwealth Games in Scotland will help to propel the country towards backing independence in next month's referendum, the country's deputy first minister has claimed.

As the Games close, Nicola Sturgeon said the record-breaking medal haul of Scotland's athletes at the globally acclaimed event had imbued voters with confidence in their country. While insisting that she was not making any "grand claims" for the impact of the Games, Sturgeon suggested they had provided a perfect platform for a yes campaign victory.

In an exclusive interview with the Observer, Sturgeon, who is leading the SNP's yes campaign, said: "I do think the momentum is with us. I think, as we come out of the Commonwealth Games at the weekend, that is us in the final straight of the campaign and you will see that momentum quite visibly."

Asked about the impact of the Games on the referendum, she suggested that while any impact would be indirect, voters in Scotland had been instilled with a renewed belief in the country's potential for going it alone. "I think it will inevitably leave a feelgood factor," she said. "I think confidence not only in Glasgow but across the country is high.

"Not only have we staged already what is being talked about as the best Commonwealth Games ever, but the team has done incredibly well with a record number of medals. But sport is sport, politics is politics."

In a strikingly upbeat interview before Tuesday's televised debate between Scotland's first minister, Alex Salmond, and former chancellor Alistair Darling, Sturgeon also stated that:

■ The yes team's thousands of volunteers could prove decisive in turning enough minds in the closing weeks of the campaign.

■ An independent Scotland would block David Cameron's "narrow-minded, Ukip-driven" reform agenda in the EU.

■ The Scottish people had been repeatedly misled about the size and potential of oil reserves in the North Sea.

The yes campaign faces an uphill struggle with the latest polls, putting the no campaign ahead by 57% to 43% when don't knows are excluded. Public opinion has remained remarkably unchanged since March. An Observer/Opinium poll of nearly 2,000 adults from across Britain found that 54% of respondents believe Scotland will vote to stay while 27% think it will vote to leave. One in five British voters believes that the success of the Commonwealth Games makes Scottish independence more likely, while 47% think the opposite.

Sturgeon said that the SNP's remarkable feat in 2011 in coming from 20 points behind Labour in the polls to 5 points ahead to form the Scottish government "demonstrates that it can be done".

She said: "There was some polling some months back that, differently to normal elections, people's source of information was not from the media but from family, friends and the people they worked with. The conversations taking place at that level are changing minds. So having a campaign in strength on the ground, as we do, is potentially very, very influential and, perhaps, decisive."

Sturgeon said that she was "hugely optimistic" about the prospects of victory and that the contest was now "very close". She added that a risk of the UK leaving the EU in a 2017 referendum would motivate some voters to support independence. She warned that an independent Scotland would block Cameron's reform agenda in the EU, including changes to the principle of free movement of people.

She said: "Free movement is an integral principle of the single market. There are issues of conditions in terms of benefits and such like, but one of the weaknesses of David Cameron's position is that the specifics of what he is trying to achieve are very vague.

"An independent Scotland would be a very constructive partner on the European and world stage and we would look to build alliances where it is right for Scotland. You know, we are not going to be part of this narrow-minded, Ukip-driven agenda of David Cameron.

"We will take positions on these things that we consider right, proper and in the Scottish interest."

On the matter of oil reserves in the North Sea, Sturgeon said that it would not be crucial to an independent Scotland but that it was a "big, big bonus". She said: "Oil and the value of oil has been downplayed from the day it was discovered by Westminster governments who want to keep the resources to themselves. I will be measured in my language: people in Scotland have been misled over decades. We have a choice now: are we happy for that to continue, for our oil revenues to be squandered? Or do we want, with the remainder that we have got, to steward them better?"

Sturgeon said she believed that the referendum debate so far had energised the country and she disowned the so-called cybernats who have been accused of trolling supporters of Scotland staying within the UK.

She said: "It's not one-way traffic. Looking at the bowels of my Twitter feed on the average day would probably make your hair curl.

"I try not to do that. So, I get my share of abuse. It is on both sides. [But] anybody who professes to be on the yes side who thinks they are doing the yes campaign any favours by engaging in cybernattery, they are not. And they should stop."