Sri Lanka beat Bangladesh by 37 runs in the opening qualifier under lights here on Saturday, but their bowling left a lot to be desired.
They conceded 36 extras, the second-highest contributor in Bangladesh's total of 265-9, after posting a challenging 302-8. Their bowlers sent down 21 wides and eight no-balls.
Sri Lanka's total owed much of its substance to young opener Upul Tharanga's brilliant 105 off 129 balls with the help of one six and 11 fours.
"We did not play our A class game and there are certain areas where we have to improve and we will do that in remaining games," said Jayawardene.
Sri Lanka play Zimbabwe at Ahmedabad on October 10 and defending champions West Indies on October 14 at Mumbai in their last two qualifying matches.
The top two sides will advance to the main draw that features world champions Australia, England, India, South Africa, New Zealand and Pakistan.
Jayawardene said his team did not perform up to the mark in the opening game because they had not played much international cricket in recent months.
They played their last full one-day international three months ago.
"We didn't play a smart game, especially in the second half of their innings but we have not played many one-dayers recently and that was one of the reasons why we were not able to perform to our potential," he said.
The Sri Lankan skipper didn't blame the dew for his bowlers' below-par performance when they fielded under lights at the Punjab Cricket Association stadium.
"The dew came on only around 8.30 pm and by that time the spinners had nearly bowled their overs," he said.
"We have to expect such things in day-night matches. I think it is good that we fielded in the evening. It will give us an idea what to expect in remaining matches."
Bangladesh captain Habibul Bashar defended his decision to field first after winning the toss, saying his bowlers failed to make the most of conditions in early stages.
"It was a good toss to win," he said.
"There was grass on the wicket, but we didn't put the ball in the right areas in the opening 10 overs."
Seamers Mashrafe Mortaza, Syed Rasel and Farhad Reza failed to get early wickets and went on to concede 188 runs in 28 overs.
"In the end, the target proved too high for us," said Bashar, whose team still managed to post their highest-ever total against Sri Lanka in 18 one-day internationals.
The Sri Lankan captain, however, said he would have batted first had he won the toss.
"It was a good wicket to bat on. I think it is always better to set a target when you play against teams like Bangladesh," said Jayawardene.
Bangladesh will now meet the West Indies on October 11 and Zimbabwe on October 13 at Jaipur.