The Italian told reporters ahead of City's trip to Newcastle United on Saturday, which Barry will miss, that match officials should understand how players might feel after Manchester United had beaten them 3-2 in the derby with a last-minute goal by Robin van Persie.
Barry was banned for using foul and abusive language at the end of Sunday's game to a match official, identified by Mancini as Clattenburg.
The official was embroiled in a high-profile controversy with Chelsea earlier in the season when he was accused of making a racist remark towards John Obi Mikel. Clattenburg was cleared of the charges after being sidelined for a month.
"Gareth is a serious man and a serious player and I don't understand why Clattenburg wrote or said these things about Gareth Barry," said Mancini of last weekend's incident at the Etihad Stadium.
"I don't know if it comes from this problem after Chelsea, but I think every fourth official should understand that at the end of a game that you lose in the last seconds.
"If he [Barry] said inappropriate words against Clattenburg, I think he [the official] should understand this," added Mancini.
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