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Morelos and Brown got into it after the Colombian was adjudged to have fouled the Celtic skipper by referee John Beaton.
The pair shared words after the incident and Morelos gave Brown a slap on the back of the head, prompting the midfielder to call him a "f****** d*******".
Morelos escaped unpunished but was later booked after a coming together with on-loan Brighton defender Shane Duffy, with Rangers going onto win the match 2-0 and go four points clear at the top of the table.
Despite admitting that Rangers deserved the win, Sutton claimed Morelos was lucky not to have been sent off, tweeting: "Rangers the better team and deservedly ahead…not so sure Morelos should still be on the pitch."
Former Manchester United midfielder Darren Fletcher echoed Sutton's thoughts on Morelos, telling Sky Sports: "This is the way he plays; he is always on the edge.
"Until you give him a yellow card, he is going to keep doing these niggly things. He’s very lucky here though [with the Brown slap], very very lucky.
"There’s nothing it and Scott Brown doesn’t react, but you could let your teammates down. He got sent off here last season when they won, and he has got to be really careful."
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Reflecting further on the derby, Sutton told BBC Radio 5 Live's 606: "Rangers thoroughly deserved their victory. I can moan all evening about Celtic having so many players out but the players who played should have performed better.
"I thought Celtic were gutless. The scoreline flattered Celtic and Rangers deserved to win by more. That's the truth. At 2-0 Rangers deserved to win by more."