He was struck on the back of the head in the seventh over and needed support from fielder George Bailey, then sat on the ground to receive treatment.
Morgan played no further part, with James Taylor taking on the captaincy.
"He's got a lump on his head, but he's fine," said coach Trevor Bayliss.
"He's got a bit of a headache but he's up and about now and having a chat.
"When anyone gets hit it's an anxious moment, but the fact he walked off the field was a good sign. He was dizzy for a while and took an hour or so to come good. I'm sure the medical staff will keep a close eye on him."
The hosts had already slipped to 22-3 in the deciding game when Morgan was replaced by Jonny Bairstow. They went on to lose by eight wickets.
The blow to Morgan, who was wearing a helmet, caused immediate concern for the visiting players, less than a year after the death of Phillip Hughes, the Australia batsman who passed away after being struck on the neck by a bouncer.
The fielders immediately went to help Morgan, while a shaken Starc was comforted by captain Steve Smith, coach Darren Lehmann, team-mate John Hastings and Morgan's batting partner Ben Stokes.
"There were a couple of guys that were a little bit shaken up, Starcy in particular," said Smith.
"It was a tough summer for us back home, losing a close mate. Whenever anyone gets hit like that, your first concern is for their health. Mine is that for Eoin, I hope he's OK and can recover well."
The new Australia skipper added: "I don't think anyone ever means to do anything like that. It is part of the game to bowl bouncers.
"You have to get back on the shop as quickly as possible, you still have got a job to do. You need to take it out of your mind, but you don't like seeing anyone get hit like that."
England captain Eoin Morgan retired hurt with concussion after he was hit on the head by a Mitchell Starc bouncer as they lost the final one-dayer against Australia at Old Trafford.