Daniel Sturridge, who scored as the first leg was drawn 1-1 at Stamford Bridge, was missing for City.
The striker missed out after picking up a knee injury in the first team's 2-1 win at Sunderland on Saturday.
Chelsea were contesting their first Youth Cup final for 47 years, but they finished with 10 men after Mellis was sent off for a late challenge on City's Kieran Trippier, who had to be stretchered off.
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