Sri Lanka have not won any of the 14 matches they have played in India since their first Test visit in 1982.
"For us we are under no pressure. We know we haven't won here and for us we need to try and change that," Sangakkara told a news conference.
"We are here to relax, enjoy and not worry about history and try and put as much pressure on the Indians as possible.
"We have lot of work to do but we are here to do well and try to win and change all this never-winning-a-test-match in India. The responsibility is on India to stop us from doing that."
Sri Lanka will play three Tests, five one-day internationals and two Twenty20 matches over two months. They will play a three-day warm-up game from Wednesday before the opening Test in Ahmedabad on November 16-20.
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