Scotland defeated France and England in the RBS 6 Nations Championship this year before warming up for the trip to South Africa with a 66-19 win over the Barbarians last week.
Now the Edinburgh Gunners centre believes the resurgence enjoyed by Scotland under head coach Frank Hadden has led to greater expectations among fans.
Di Rollo said: "We have enjoyed a great revival in recent months, but that is exactly why we will be under an enormous amount of pressure.
"The more you win, the greater the pressure. When we played France in the Six Nations, there were no expectations at all and we could just go out and play.
"But, by the time we came to play England, the crowd were up for the game because they thought we had a good chance. It is hard for people not to get carried away.
"We have a decent chance, but one thing is certain - we are not going to wipe the Boks off the pitch."
But the 28-year-old maintains preparations have been good for the Scots.
Di Rollo added: "We have a good feel for how they will come at us.
"Sometimes, you can have good preparation and can't stop the opposition, but we are confident we are equipped to deal with them.
"We are organising ourselves much faster than even at the start of the Six Nations and that is a massive key to good defence.
"If you are in position, it is hard for the opposition to smash through and they will have to try moving the ball.
"We know about the South African blitz defence and we have a couple of ploys to get the ball to the outside.
"We have done a lot of general kicking to get the ball behind them.
"It is a defence we have seen a lot with Edinburgh, the Ospreys use it and the Dragons did when Percy Montgomery was there. It is a thing we have learned to deal with.
"The game that suits Scotland is getting the ball wide, but, when we played Wasps in the Heineken Cup, there was a lot more tactical kicking than normal and it worked."