The head of a Boston ad agency axed from a lucrative state promotion contract by the administration of Gov. Charlie Baker blamed the decision on budget cuts — not questions over his firm getting millions in off-budget payments from former Gov. Deval Patrick.Steve Connelly, president of Connelly Partners, said he was told by Baker aides that “the budget was cut to zero and all the tourism money had to be terminated.”The Herald reported yesterday that the Baker administration ended the ad firm’s work at the end of last month.