The striker was caught up in controversy after lashing out at Bluebirds midfielder Jordon Mutch but escaped with just a caution.
The striker was only booked after kicking out at Bluebirds midfielder Jordon Mutch before opening the scoring with a quarter of an hour played.
He remained at the center of the action, sending in the left-wing corner from which Patrice Evra restored United's advantage following a coolly taken equalizer from the excellent Fraizer Campbell.
Substitute Kim Bo-Kyung sent the Cardiff City Stadium into raptures with a stoppage-time equalizer, but much of the post-match conversation focused on Rooney's early rush of blood, and Moyes felt referee Neil Swarbrick was right to display leniency.
"I didn't think so," Moyes told Sky Sports when asked whether Rooney should have been sent off. "I thought that the boy runs across his path and there's a bit of a tussle but I didn't think it deserved any more than a yellow card. I think there's lashing out at times and I don't think that was a lash out in any way. It was more him feeling that he'd been hard done by with the boy running across his path of the ball.
"I didn't think it was a lashing out to cause any harm. It was more of a disappointment that he'd lost the ball."
Cardiff defender Ben Turner cut a relieved figure after his error led to United's opener but insisted Rooney had the right to be on the pitch to capitalize on his misfortune.
"I do think he kicked out from where I was but I think the way the game's going I didn't want him sent off," he told Sky Sports. "It's becoming less and less of a physical game, and I think we need to keep some of that element in the game for the enjoyment of the fans.
"I think it's nice to have a bit of that going on."
Turner's manager Malky Mackay agreed that a yellow card was "sufficient" with regards to Rooney before addressing another moment of controversy surrounding his midfielder Gary Medel.
Peter Whittingham's free kick that led to Kim's late leveller was retaken due to an altercation between Marouane Fellaini and Medel, during which the Chile midfielder appeared to slap the United man across the face, and Mackay felt both players shared the guilt.
"He could [have been sent off] but I also look at Fellaini doing what he does normally, putting his head in someone else's face, and that's, for me, a sending off. So that's something that needs to be looked at as well," he said. "Having seen the way Fellaini marked and used his arms at times in the game - not at all times but at certain points - but more so putting his head into someone's face, I think that also justifies having a look at."
Moyes was understandably aggrieved but was also critical of his team's defending from Whittingham's set piece.
He added: "If you slap somebody in the face you would expect some action to be taken and we actually lost our concentration because we're set up for the free kick, the referee goes away and spends a minute or so talking to them and sets it back up.
"We still should do better, but it gave them two bites at the cherry because they'd actually delivered the first ball. It gave [Whittingham] another chance to get his sighters in and he certainly put in a good ball."