The Norwich City loanee was forced off the field in the 66th minute after battling against injury at Wembley Stadium.
With the scores locked at 0-0, the 22-year-old was furious that he could not remain on the field.
It is understood that Morris had tried to play on after suffering with a knee injury in the second half.
Shrewsbury fans turned to Twitter to praise the English ace after his explosive outburst on the touchline.
One labelled him as a "warrior", while another added: "Raw emotion showed there by Carlton Morris."
Morris returned to the pitch to get his squad ready for extra time after the final whistle blew at 1-1.
But Richard Wood found the net in extra time to secure promotion for the Millers after just one season in League One.
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Shrewsbury, who finished five points behind Rotherham in the league, are yet to win in five attempts at Wembley.
Morris could return to the Canaries this summer after bagging 10 goals in 53 appearances this term.
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