The party's leader at Westminster also said he believed that most of the "don't knows" wanted to be persuaded of the case for independence.
Asked about the controversial Cybernats (online activists), the 44-year-old politician urged all sides to take care in the language they used and show respect to their opponents.
Recent polls have shown a marked fall-off in those who said they still do not know how they would vote on September 18. The four most recent ones have recorded don't knows at 13%, 12%, 11% and 16%. In December, one poll placed them as high as 33%.
But Mr Robertson, who pays close attention to internal polling and campaign intelligence, believes the number of undecideds among Scotland's four million voters is much larger than recent snapshots have suggested.
Asked his estimate for the don't knows, he replied: "Up to 40% of the electorate are reachable. How one chooses to describe the degree of undecidedness I will leave to the psephologists.
"Most of them wish to be persuaded of the strongest case for Yes, so they can, if they want to, vote that way."
Asked if he was really getting a sense on the ground of this desire to be persuaded in favour of independence, he said: "Yes. People want to get a satisfactory balance between their head and their heart when they are undecided."
The MP for Moray, who co-ordinated the SNP's successful campaign in 2011 that resulted in a landslide victory for the party at Holyrood, stressed: "I am totally convinced the referendum is there to be won. It comes down to confidence, optimism and doing everything that we need to do to provide voters with the information that they require to vote Yes."
Asked about whether the Cybernats enhanced or diminished the campaign, he said: "Anybody who uses extreme language or is disrespectful from any perspective diminishes the democratic process.
"One persuades people by being respectful and explaining that this better future for Scotland is for everybody regardless of where their views were ... The point about the discourse we choose and the way in which we choose to make our case is really important."
Marking just six months to polling day, Nicola Sturgeon has set out six reasons for voting Yes, including creating more jobs and opportunities for Scotland as well as protecting public services from "Westminster's privatisation obsession".
"The referendum is a choice between taking Scotland's future into Scotland's hands or leaving our future in the hands of an out-of-touch Westminster establishment," the Deputy First Minister says today.
Elsewhere, Alistair Darling has set out the pro-UK camp's "positive campaign with a message of working together at its heart".
"The history of the UK shows we are better and stronger when our four nations pool and share our resources by working together. The bailout of RBS is a good example of that."
The Better Together leader today adds: "We can decide to keep the strength, stability and security of being part of the larger UK, with a stronger Scottish Parliament and the guarantee of more powers, or we can take a leap into the unknown with all the risks of separation."