Murphy represented the Republic of Ireland Under-16 team at the 2000 UEFA European Under-16 Football Championship and the Under-19 team at the 2002 UEFA European Under-19 Football Championship. He was a regular in the Ireland under-19 squad under Brian Kerr and was preferred to Aston Villa goalkeeper Wayne Henderson for the European under-19 Championships qualifiers and finals in 2002 until a shoulder injury allowed Henderson to reclaim his place. He has been capped since at under-20 and under-21 levels.
Murphy spent four seasons with Manchester City where the competition for the number one jersey included David Seaman, Nicky Weaver and Carlo Nash, but made the 1st team bench on a number of occasions in the old 1st Division (second tier) and the Premier League. Loaned out to Oldham Athletic in 2002–03, he made his senior début during a loan period with Peterborough United that same season away to Brentford in League One in May 2003.
Brian Flynn signed him for Swansea City on a free transfer two months later, and he made 13 appearances for the club during the 2003–04 season. He was kept out of the first team in the following two seasons by the form of Frenchman Willy Gueret.
Murphy ended rumours linking him to Bristol City by signing an improved contract at Bohemians in November 2007.
Murphy impressed in that game, especially when he denied the Owls with a close range, reflex save in the first half. He retained his place in goal for the next game with Scunthorpe only conceding one goal. His home debut came against Bristol City on 27 January 2010, making one extremely memorable and spectacular save from David Clarkson. Indeed, it turned out to be a game for the goalkeepers, because for all Ipswich dominated, it was Murphy's opposite number, Dean Gerken who stole the headlines with a spectacular performance that included five world class saves.
On 7 May 2011 it was confirmed that Murphy had rejected a new contract and would be leaving the club.
After impressing on trial Murphy signed a two-year deal with Queens Park Rangers. He made his first start for the club in a 2–0 loss to Rochdale in the League Cup. Despite only playing once in his first two seasons, Murphy signed a new two-year deal following the club's relegation.
On 8 August 2015 Murphy signed a deal until January with Portsmouth, making his debut for the club in a 3–0 home win against Dagenham & Redbridge on the same day.
On 2 September 2016, Murphy joined Football League Championship side Cardiff City.
