"It's another big challenge for us," Jaywardene said after Sri Lanka bowled out Pakistan for 75 runs in just 22.5 overs in reply to its imposing total of 309-5.
Sri Lanka has been in good form since winning the Asia Cup in Pakistan last July. It defeated India in a home Test series before beating Zimbabwe in a limited-overs series, and also recorded victories over Bangladesh in both Test and One-day series.
However, the Sri Lankans lost the One-day series to India at home shortly after the Asia Cup.
"That's something that really hurt us and hopefully we will turn things around," Jaywardene said.
Sri Lanka is due to play India in a five-match series starting next week before returning to Pakistan for two Tests. It agreed to tour Pakistan in two stages after India canceled its tour in the wake of the terrorist attacks in Mumbai.
Sri Lanka lost to Pakistan in the first of back-to-back matches in Karachi by eight wickets. It then won the second match by 129 runs before inflicting Pakistan's worst ODI defeat by runs.
Tillakaratne Dilshan in his new role as opening batsman led the Sri Lankan revival in the series with the scores of 42, 76 and 137 not out, earning the man-of-the-match award with his last two innings.
"Dilshan has been a very versatile cricketer for us," Jayawardene said. "He's been given the opportunity and he has grabbed it with both hands. Now, it's a good competition among the openers."
Prior to the series, all eyes were focused on Sri Lanka's spinning pair of Muttiah Muralitharan and Ajantha Mendis. However, Sri Lanka dispatched the Pakistan top-order batsmen through pace bowlers Thilan Thushara and Nuwan Kalusekera.
"They have been unsung heroes for quite some time," Jayawardene said of the two. "Our pace attack has been really good for the last two to three years and these guys have been pushing each other."