The England international was dismissed for a second bookable offence after blocking Daniel Agger's run in the 72nd minute. It did not affect the outcome of the match as James Milner's penalty after Barry's red card completed victory after Sergio Aguero and Yaya Toure had given them a comfortable half-time lead.
"I did not agree with the referee for the second yellow card," Mancini said. "I didn't understand. I watched the games yesterday and there were a lot of tackles without yellow cards. You play one important game like this evening and we lose one player for nothing."
After taking just one point from their last two matches Mancini was pleased to return to winning ways.
"We were unlucky to lose at Sunderland but tonight I think, even though we had some problems in the second half, it was a good performance," he said.
Liverpool manager Kenny Dalglish was unhappy with elements of the performance but did not think his side deserved to be 3-0 losers.
"I am not so sure the scoreline reflects the way the game went," said the Scot. "I am not saying we deserved to win but the lesson we learned tonight was if we are not clinical we are going to suffer.
"There are a lot of things that happened tonight which we can correct by ourselves and we have to go and do that.
"We had a great opportunity to open the scoring (through Stewart Downing), we conceded the first goal after we lost possession, the second was a corner which we'd had a warning seconds before it and the third was when they were down to 10 men and Toure has run the length of the field and won a penalty.
"It is a harsh lesson but we will learn from it."