Karne Hesketh crossed in the final minute to win the World Cup Pool B encounter in Brighton on Saturday.
The Brave Blossoms face Scotland on Wednesday in their second match.
"We have two objectives: reach the quarter-finals and be team of the tournament," said Jones.
"With that in mind we have made a successful start. We did not come here to be one-hit wonders."
Japan, who were given a guard of honour as they left their Brighton hotel in the wake of their win over the Springboks, have had just four days to prepare for Wednesday's match.