Midfielder Barry made 653 appearances in lengthy spells with Aston Villa, Manchester City and Everton, scoring 53 goals.
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The hosts ultimately fell short of ending what is now a club-record 17-match winless streak across all competitions, with United holding on for a third consecutive away win and a sixth victory in their last seven outings
Raheem Sterling sealed the game in the second half after City had emerged with a slender lead from a whirlwind spell of three goals inside five minutes
Team captain Evans was taken off with a groin problem, while Barry was withdrawn early in the second half due to a back strain.