But in stoppage time Dzeko and then Sergio Aguero netted to turn the entire campaign on its head and end City's 44-year wait for a league title.
"At 2-1 down I was thinking this is done," Barry said.
"I looked up and saw a helicopter and wondered if it was the main trophy being flown north.
"Towards the end, I was sitting there watching our fans leaving, just thinking 'Here we go again'.
"In a way, it makes it more special but I would have preferred an easier win."