Sri Lanka has not won a Test in their last 11 outings, since beating India in Galle in July 2010 when world bowling record holder Muttiah Muralitharan made his final appearance.
This year, Sri Lanka lost an away series against England 1-0, before falling to Australia by a similar margin at home.
Dilshan said he looked forward to turning the tide when they clash with Pakistan in a three-Test series which opens at the neutral venue of Abu Dhabi on October 18.
"The important thing is to remain patient. We have got some inexperienced bowlers and it takes time for them to develop," Dilshan told the Colombo-based Island newspaper.
"If you take the last series against Australia, we lost one Test that could have gone either way. I thought we played well in the remaining two Tests."
Dilshan said the team needs time to overcome the absence of the retired duo of Muralitharan and Chaminda Vaas.
"Guys like Murali and Vaasy did an exceptional job for us for 15 years," he said. "Suddenly when you lose them the team struggles. I believe we need to be patient rather than take harsh decisions."
Injured fast bowler Nuwan Pradeep returns to the bowling attack, which also includes off-spinner Suraj Randiv and left-arm spinner Rangana Herath.
Dilshan predicted a close contest against Pakistan. The Tests will be followed by five one-day internationals and a Twenty20 match.
"I feel they have a balanced side," the captain said. "The wickets will be batsmen friendly and the big challenge for us will be to take 20 wickets in a game."
The Sri Lankans leave for the UAE on Friday.
Pakistan has been forced to host international matches in neutral countries after a terrorist attack on the Sri Lankan team bus in Lahore in March 2009.
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