The City star was first at the forefront of controversy as he was late in a challenge on Arsenal's Martin Odegaard before clattering into Declan Rice minutes later.
The challenge on Odegaard was reviewed for a red card, however, talkSPORT understands this is not viewed as a clear and obvious error.
But following Kovacic's challenge on Rice, Oliver opted not to give him a second booking, sparking criticism from fans, who drew comparisons to recent similar incidents with Liverpool's Curtis Jones and Chelsea's Malo Gusto.
Both players were sent off for their respective clubs but Kovacic avoided red for City, with a lack of consistency being raised.
Speaking on commentary for talkSPORT, Alex Crook said: "You don't know what you're doing is the cry from the Arsenal fans.
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"Didn't get near the ball, it is a definite second yellow, for me Michael Oliver completely bottled it."
Former Arsenal star Perry Groves added: "It was 100 per cent a second yellow card. I'm a big fan of Michael Oliver but he's completely bottled it."
Taking to X, one fan said: "If Jones was a red card last week that's a red card every day of the week. F****** consistency is all I ask for.... Far more dangerous challenge from Kovacic."
"Gusto is currently suspended for a challenge nowhere near as bad as Kovacic's. Consistency from PGMOL? Never," added another.
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A third said: "I hate, hate, hate refereeing in this country. If Curtis Jones' challenge last week [he got the ball first, by the way] is a red card then that tackle from Kovacic has to be as well. The lack of consistency is maddening."
"That Kovacic tackle is MILES worse than the Jones one last week. We just want consistency," added a fourth.