"I think the conditions will be different at different venues and we have to make sure we don't sit back on what we have achieved now.
"We now need to work much harder, improve ourselves and adapt to the other conditions," he added.
"We had a set of plans for this group stage, how we wanted to play our cricket, especially in Trinidad, and we executed them very well."
Victory was sweeter for Sri Lanka, after losing eight of their last 10 one-day internationals in India.
"Any side at home is stronger. If you take us in Sri Lanka, we are much stronger than anybody. You know the wickets and you have the support of the crowds," he said.
"When India are playing at home, they have 30,000-40,000 in most of the stadiums, and in Kolkata you have 80,000 shouting for you. So it is totally different.
"That is why I said when you guys asked me in India that we are playing India in the World Cup and I said 'Yes, but not in India. We are playing in the Caribbean'."
Jayawardene said his team's recent good performances away from home had prepared them well for the World Cup.
"What we tried to do over the last year or so is that we tried to play a lot of cricket away from home," he said.
"The practice that we have been doing over the last 12 months has groomed us to compete abroad, get adjusted to wickets and conditions quickly and play some smart cricket."
Winning habits
The Sri Lankan captain said his team now had a chance to go for glory in the Super Eights, especially after carrying two points into the next round.
"When we started, everyone was talking about this being the 'Group of Death', so, to carry two points is brilliant," said Jayawardene.
"We just have to make sure we take one game at a time, like we did in this group.
"I reckon three or four wins will probably secure a spot in the last four. But we don't want to look at it that way because if you are winning, it is a very good habit to have."