Anderson (1-67) thought he had caught the edge of Haddin when on 9, but TV umpire Tony Hill turned down Cook's referral after ruling the ball had hit both pads and not the bat.
England made three changes for the fifth test with Scott Borthwick, Boyd Rankin and Gary Ballance all making their test debuts as the tourists were attempting to avoid a repeat of the humiliating 5-0 whitewash from the 2006-07 Ashes series.
Australia made no changes to the XI that convincingly won the first four tests and regained the Ashes, becoming just the fourth team to keep the same lineup in each match of a five-test series.
Only England against Australia in 1884-85, South Africa against England in 1905-06 and West Indies against Australia in 1991 achieved the feat.
Cook won his first toss of the series and sent Australia in to bat on a green-tinged SCG pitch and was rewarded with four wickets in the opening session, with Stokes taking two and Anderson and Stuart Broad one apiece.
