Yanga-Mbiwa was dismissed five minutes before half-time in Saturday's Premier League clash at St James' Park when he pulled back Luis Suarez in the penalty area and Steven Gerrard drew Liverpool level for the first time from the spot.
"I thought it was a tough call today," said Pardew. "I don't think Mapou really pulled him down in a manner that was a definite sending-off.
"He got a little piece of him, he was the last man and I suppose by the letter of the law, he had to go. I haven't got a massive problem with it."
Newcastle had earlier taken the lead through Yohan Cabaye's long-range shot before substitute Paul Dummett's first goal for the club restored the hosts' advantage.
Daniel Sturridge headed Liverpool's second equaliser before Suarez struck the crossbar and then produced a flying save from Tim Krul with almost the final kick of the game.
Pardew was delighted with the resilience shown by his team in front of an appreciative home crowd on a day when several hundred fans had earlier staged a march to protest about owner Mike Ashley's running of the club.
He said: "We showed today that that is in the group, that we can fight when we need to and therefore I am immensely proud of the whole day, really.
"Our fans were brilliant - Steven Gerrard coming to take a corner and being applauded by our fans and stuff like that, it was just a great day for football.
"If Brendan is slightly disappointed, he shouldn't be because he's got a good team and I think we perhaps just deserved the point.
"I enjoyed Paul Dummett's goal because we have had him since he was nine.
"Paul has had to come through some really good class players here to get as close as he has to get that opportunity he got today.
"It's great for the academy and great for us that he scored that goal, and his little bunny-hop after was even funnier, so he'll get a bit of teasing about that."