"I have always described the games against the Netherlands and Scotland as two scary games and we don't want any slip-ups in these games," Arthur told reporters at team's hotel on Tuesday.
South Africa, who recently deposed world champions Australia as the world's top team, had their first work-out at the Conaree stadium at the outskirts of Basseterre on Tuesday.
They open their campaign with Group A match against the Netherlands on Friday.
Defending champions Australia and Scotland, the two teams in Group A, meet on Wednesday.
South Africa, who have never won the World Cup since their re-admittance in international cricket in 1992, had a lacklustre build-up to the tournament as they struggled in their warm-up matches.
They were given some worrying moments by debutants Ireland before they managed to register an unimpressive 35-run win. They then went down to Pakistan by seven wickets in their second warm-up match.
Arthur, however, believed the real competition would mean something else to his team.
"We have given the guys a little bit of leeway up until now, but this is now time to start the real competition and we are really keen that it gets underway," said Arthur.
South Africa's real test will come against Australia on March 24 in a match which decide who tops the Group A. The top two teams advance to the next round Super Eights with the winners of that crucial match taking their points with them into the second stage.
Captain Graeme Smith described their position as the world's best side as something to be proud of.
"Quite naturally we are extremely proud of the number one ranking, but that was built up over two years of playing good and tough cricket and we need to do the same in the World Cup," said Smith, who was not amused at being tagged as chokers.
"The chokers' tag is something we have always struggled to get rid of. It is something this team has found quite amusing at times. This team has played perfectly well under pressure and will continue to do so," said Smith.