Dugdale, 29, spent a year at the National League club, making 20 appearances and scoring two goals.
Liverpool-born Dugdale, whose previous clubs include Morecambe and Tranmere, posted on Twitter that "the distance from home and my young family was too much."
Left-back Cole, 23, was recently transfer-listed having signed from Staines Town in January.
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Defenders Adam Dugdale and Chinua Cole have left Eastleigh by mutual consent.