Heading into day five, the hosts in Galle are 110-1 - requiring another 260 runs for victory for what would be Sri Lanka's highest successful fourth-innings chase.
Despite the highest winning total from a team batting last at the Galle International Stadium sitting at a lowly 96, the former Sri Lankan opener is confident his men are capable of breaking new ground.
"I haven't seen that stat, but that is something I'll look into and probably have in the dressing room for all of us to be motivated," Atapattu said.
"It's good to know that people have done it, but even if someone hasn't done it - it doesn't mean that you can't do it.
"It's all in the mind and how you think and the confidence levels. In a situation when you have the whole day to get the runs - don't get me wrong, it's not easy or guaranteed with the attack they have - but there is a chance.
"It's a bold declaration from [Hashim] Amla, encouraging us to go for our shots."
Atapattu conceded the Proteas' lead of 369 runs heading into the fourth innings was daunting, but his charges were confident from the outset - with Kumar Sangakkara (58) and Kaushal Silva (37) the men unbeaten heading into Sunday's deciding day.
"It's a challenging total," he said.
"A team hasn't gone past 300 in the fourth innings at this venue, but we've got a team inside the dressing room who're willing to fight. That I can guarantee you.
"We're aiming to get the amount of runs but we'll fight to get through the first session tomorrow and see where we'll be placed at."
Atapattu said the notion of the Galle wicket being a spinning one was a misnomer created by all-time leading Test wicket-taker Muttiah Muralitharan.
"This wicket has turned square when Muttiah Muralitharan bowled here and he would have turned it square on any wicket. Some of us had been misled," Atapattu said.
"Yes the wicket is good and the batsmen have adapted, used their feet, swept, reserve swept, handled situations, and handled bowlers differently, because there's no bowler called Murali.
"He would have been in a different proposition had he been here."