Derry's defence of the EA Sports League Cup ended at the first hurdle on Monday afternoon with this defeat by Galway at Terryland Park.
United dominated throughout against an under-strength City side and took a deserved lead on 35 minutes.
Dave Cooke fired home after Jay O'Shea's free-kick was blocked by the Derry wall.
Galway wasted a series of chances and O'Shea hit the woodwork as they secured a place in the quarter-finals.
The Candystripes went into the game on the back of a confidence boosting 3-0 away victory over Drogheda United at United Park on Friday night.
Derry defeated Wexford Youths 6-1 in last year's League Cup final.
City have won the competition for the past four seasons.
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