Milner, who was pressed into action as an emergency right-back after a spate of injuries at Liverpool, was sent off for a foul on Wilfried Zaha in the closing stages of the match.
He went straight down the tunnel after mistiming his tackle and will miss Liverpool's next game against Leicester City.
Moss, who taught Milner about 20 years ago, also coached the youth team in which the England international played.
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The picture, which the Premier League has confirmed to be genuine, shows a baby-faced Milner seated in the front row of a team photo holding a football, with Moss standing beside his young charges with his hands behind his back.
(Reporting by Simon Jennings in Bengaluru; Editing by Hugh Lawson)
