Adam Johnson and Carlos Tevez both hit the net inside the first quarter-hour, blowing the visitors’ gameplan out of the window.
David Silva, Patrick Vieira and Yaya Toure added goals in the second half for City, who moved above Chelsea with the win.
It was a tough first game back for Turner, who made his first appearance since sustaining a knee injury against Everton in November.
“Obviously we’re all disappointed with how the game’s gone,” he said. “We wanted to come here and shut up shop early on so giving away two early goals has killed us.
“From that point on we were always up against it.
“We started the second half quite well but then conceded a couple more. It was a bad day at the office.”
Turner’s luck was summed up when City added their third goal through Silva, who pounced on an unfortunate deflection off the centre back to prod home.
Turner is hoping to help his side get back on track next weekend when West Brom visit Wearside. “Saturday’s game is a big one,” he said. “If we keep working hard things will come good again.”