Roberts describes the game as "the biggest in the club's history".
Stevenage have enjoyed a meteoric rise over the last few years, climbing up from the Conference in the summer of 2010 before being promoted to the third tier of English football last season at the first time of asking.
Having swept aside Sheffield Wednesday on Tuesday night, the Hertfordshire side are now in the play-off places in League One. On current form, they have a very good chance of achieving their third promotion in as many seasons.
Roberts, 28, concedes Sunday's challenge will be on a completely different level to any other that he has faced as skipper over the last three years.
Spurs, third in the Premier League and favourites to win the FA Cup, are the visitors to Broadhall Way, where a capacity crowd of 7,100, and the TV cameras, will greet the high-flying Londoners.
Playing against the likes of Gareth Bale, Emmanuel Adebayor and Luka Modric would normally strike fear in to the hearts of most lower-league clubs, but having beaten Newcastle in last year's competition, and disposed of Reading this year, Roberts thinks his team have every reason to be confident of causing an upset.
"It's probably the biggest game in the club's history," Roberts said.
"We have played some massive games over the last couple of years which have had more riding on them, but with it being Tottenham, it's a massive game.
"There is a belief there that we can cause an upset, though.
"We have a fantastic cup pedigree. Even back in the Conference days, we won the FA Trophy and got to the final the following season and we had a really good run last year in the FA Cup.
"We lost to Reading last year but we showed how far we have come by defeating them at our place this year.
"There have been some great results this year and hopefully we will get another one on Sunday."
The 3-1 third-round victory against Newcastle last year gave Stevenage the confidence they required to achieve promotion to League One, according to Roberts, and he hopes victory over Spurs will have a similar effect this year.
"It was a massive, historic day for the football club when we beat Newcastle," the centre-back said.
"It gave us more confidence in the league. It helped us get successive promotions and we have carried that form on in to League One this year.
"I think if we did it again it would help rub off on our confidence in the league. Some people might look at it and say it's a distraction, but we have always managed to strike the balance and if you are winning it can be good for your confidence.
"It's been good for our league form in the past and I don't see it being any different this year."
There was an air of excitement around Stevenage's training ground on Thursday as the club opened their doors to an unprecedented amount of camera crews and photographers ahead of Sunday's game.
Few would begrudge the team from enjoying the moment - after all, the club nearly went out of business in 1999 before current chairman Phil Wallace took over.
Despite their small fanbase, Roberts insists the club has the potential to keep on climbing the leagues.
"Every time we achieve something, every time we win our next medal, there's hunger there again to win another one," Roberts added.
"A lot of clubs just stay in the league or are happy with just being mid-table, but we are always striving for the best at this club. It's definitely a club on the up."