Singh and Yousaf Raza Gilani held brief talks during the match, which India won, as the two leaders used the fixture to promote better ties between their rival countries.
India and Pakistan "should be working together to find cooperative solutions and need permanent reconciliation to live together in dignity and honour," Singh said in a speech during the talks.
"We should put our ancient animosities behind us to attend to the problems of our nations," he said.
India's foreign secretary Nirupama Rao said that the match had "provided impetus" to efforts to re-build cross-border relations.
"The meeting reaffirmed the intention that both countries want to take the process of dialogue ahead," Rao said, adding that "both sides have the same goal of normalisation of the relationship."