Sri Lanka qualified for the Super Eights with an all-win record in group matches, showing no mercy to former champions India, Bangladesh and debutants Bermuda in Trinidad.
Jayawardene says his team's ability to compete hard is the main reason for their doing remarkably well in away one-day series in recent times.
"We win pretty well at home and we have that ruthless instinct, but we never seemed to have that kind of edge when we travelled. Over the last 15-16 months, we have developed that," he said.
Sri Lanka, who open their Super Eights campaign against South Africa here on Wednesday, won 5-0 in England last year before sharing a one-day series in New Zealand.
"We have now managed to take that ruthlessness when we are playing abroad as well. This was something we wanted to do and now it has come into our game," said the Sri Lankan skipper.
"We always had the talent to perform well, but we just could not win that many matches abroad. As a team we have realised that we have to compete harder and we have to be ruthless."
Jayawardene said his team now had the talent and confidence to win matches from tight situations.
"At home, you feel you can win a match from any situation. If you can take that when you are playing away from home and believe that you can win from any situation and that's what ruthlessness is. It's that self-belief," he said.
"You just have to focus harder. Once you have the opposition down, you have to finish off the games. If we can do it at home, I am sure we can do it away from home as well."
Jayawardene said coach Tom Moody had played a big role in making the side a highly competitive unit. His team looked the most impressive in group games, giving no chance to India, Bangladesh and Bermuda.
"Tom has brought something new to the table for us," he said.
"He has pushed us from our comfort zones and pushed us to be better players. Mentally he wanted us to be much tougher as a group."
Sri Lanka have already carried two crucial points in the second round, but Jayawardene said his team were aiming to win more than half of their matches to ensure a place in the semi-finals.
"In group matches, we wanted to win every game. It's the same here. You have to win every game you play and that will give you a lot of confidence and it will give you a lot of momentum," he said.
"It's tough to say how many wins we need in the Super Eights to make it to the semi-finals. The top six teams are battling for four places. I reckon you have to win at least half of those games, but that's minimum.
"If we win more, we can be in a comfort zone. The earlier you get those wins under your belt, the easier for you going forward. We have to make the most of the opportunities we get because things like rain could be a factor."
When asked whether it was possible to win 11 games in a row -- three in the group stage, six in the Super Eights, the semi-final and final -- the Sri Lankan captain said: "Yes, it's possible if you play good cricket.
"I am sure most of the teams who are unbeaten till now will be thinking of that. That's the only way because the more games you win, the better for your confidence. The opposition also fears you. It's all about momentum."
Sri Lanka may have lost to South Africa in the Champions Trophy in India last year, but Jayawardene said his team were looking forward to earning points against Graeme Smith's side.
"We do carry points (in the Super Eights), but we are not taking them into account," he said.
"Taking early points against South Africa will definitely benefit us, so it's a very big game for us. This is probably our turn now to win now."