Tillakaratne was appointed as an interim Test skipper after the resignation of Sanath Jayasuriya last year but won just one Test in his 10-match tenure.
"I am stepping down as captain because it is high time that someone should take over and I can concentrate on my batting," Tillakaratne told reporters.
"I have spoken to the selectors about how I feel about it and they have accepted my resignation."
"We lost the series and if someone is going to take over then this is the time to do it with so many tours coming up."
Tillakaratne was disappointed with the performance of his top order, believing that Sri Lanka needed to toughen up.
"We need to show a bit of character when the going gets tough but we were so soft and I am sure that we could have saved this match," he said.
Marvan Atapattu, the vice-captain and one-day captain, is tipped to be appointed to take over Sri Lanka's tour to Zimbabwe in mid-April.
