The Dutchman came off the Manchester United bench with the match goalless, only to hit the woodwork from 12 yards before again being denied by the upright late on.
But Moyes is certain Van Persie will not be deterred, despite failing to add to his solitary goal so far in Europe this season.
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Rooney added to PA Sport. "Most forwards in the world miss penalties and that won't affect him, I'm sure."
Chicharito was also guilty of profligacy, and United's disappointment was compounded in the closing minutes of the match when Marouane Fellaini was sent off, though remains confident of qualification for the knockout stage.
"I think it bobbles to be fair to [Chicharito], it just bobbles off the ground and he got underneath it," Moyes added.
"It shouldn't have been a draw, it should've been a victory. We played well enough to win the game."
Both manager and player alike expressed disappointment at the draw, but remain happy with United still sitting top of Group A.
Moyes continued: "We had a lot of chances and missed a penalty as well. It was [concerning] because when you get opportunities you want to take them. They would have ensured that we went well clear at the top of this group.
"I thought it was a difficult night for all our players, the referee didn't give us much.
"We're in a good position but we should have got the three points tonight. We've got two more games to come and hopefully we get the points to qualify."
Rooney added: "We're disappointed we didn't get the three points as we had the best chances. Overall, though, we can see the positives. We got a clean sheet and we're still top of the group.
"I think coming away from home in the Champions League is always difficult. But we created the better chances and I feel we should have won the game. A draw wasn't the worst result for us, though, particularly given the other game finished 0-0 as well. But we're disappointed we didn't get the three points."The Scot also leapt to the defence of Fellaini, insisting that the Belgium international was unlucky to be shown a second yellow card for a late challenge.
"I think there were some strange decisions, and that was one of them," the United boss added.
"I think it was just a case of totting up [the challenges] at the end of the day that got him the sending off. It was harsh, as he played well."