Rooney clashed with Bluebirds midfielder Jordon Mutch in the eighth minute at Cardiff City Stadium, kicking his opponent and appearing to strike him with his left arm as they began to tumble to the ground.
But referee Neil Swarbrick deemed a yellow card enough punishment, and Rooney went on to open the scoring with a turn and low finish, before his corner allowed Patrice Evra to head home United's second.
However, Cardiff twice levelled, with Fraizer Campbell finishing from a sumptuous Mutch pass against his former club, before Kim Bo-kyung headed in to earn a point in stoppage time.
Moyes felt Swarbrick had got the Rooney decision right, but believed his side had lost concentration when the referee pulled Gary Medel and Marouane Fellaini to one side, after the Chile midfielder appeared to slap the Belgian as Cardiff prepared to take the free-kick from which Kim scored.
Moyes said: "I think Mutch runs across his path and runs down the line of the ball and I think Wayne's half in motion, I don't think it is any more than a booking that's for sure."
Of the Medel incident, he added: "I think if the referee sees it, he must have stopped the game for something because, most importantly, we lost our concentration.
"They actually have delivered the first ball in, so Peter Whittingham has had the chance to cross one in as the referee is blowing up.
"So he has his sighter for the second one and I thought we lost concentration with it more than anything at that point.
"I don't know what the referee can do in that situation but I am sure he had seen something to call them out, and I just think it actually worked against us as we were set, and we didn't defend as well as we should have done on the next ball."
Cardiff manager Mackay also looked to play down the Rooney incident.
He said: "I have looked at it (the Rooney incident) again and some referees might send him off, but I thought overall Neil Swarbrick had a good game and I think he handled it well.
"I think it was two teams who were tough and committed and there were some tasty challenges throughout the whole game.
"But I think his handling of the game was reasonably good."
The Scot also backed Swarbrick's handling of Medel's confrontation with Fellaini.
He said: "Well, he (Medel) is 5ft 2in and Fellaini is 6ft 7in so he is up to his belly button.
"So his arm just about reached his shoulder and then Fellaini has his head down in his face again so I think overall looking at it the referee got it right on both counts."
However, former Liverpool and Rangers manager Graeme Souness did not share the opinion of the two managers when it came to Rooney's clash with Mutch.
Speaking on Sky Sports 1, he said: "He should be off there's no argument. Why the ref has given him a yellow card is beyond me.
"He's got a great view of it, he's keeping up with the incident all the time. If he's booked him, he's seen something. If he sees that, it's a sending off.
"I don't know what Wayne is thinking of. He's got an exploding head, we know that. That's just borne out of frustration."
United's unbeaten run now extends to 10 games but they missed out on the chance to climb into the top four and an ineffectual display, particularly in midfield, indicates there is still plenty of work ahead for manager Moyes.
And the former Everton manager, who hopes to have Robin van Persie (groin) and Nemanja Vidic (concussion) available to face Bayer Leverkusen in the Champions League in midweek, admitted his side had been below-par
"I am disappointed," he said. "It was similar to against Southampton where we had the game in our control with a minute to go and conceded from a set-piece.
"I thought we should have played better, we did not have a lot of rhythm in the second half.
"This has been a tough place to come for teams. We were on the back of having players on international duty so we would probably have taken a result however it came, but I would have liked it to be better. It wasn't to be."
Source: PA
Source: PA