A loose touch in the box from the Bosnian international provided Jesse Lingard with the chance to level the scores and secure a point for United late on.
The error came just moments after the Gunners had regained the lead via a Marcos Rojo own goal.
Emery refused to place individual blame on Kolasinac and instead praised his overall performance at Old Trafford.
"I am not frustrated. At the end Kolasinac had his head looking down and I said to Sead you had a very good match and you gave us a lot of good circumstances where we could have scored with your actions – these things can happen in defence.
"These things can happen and above all be positive and learn with this action.”
The draw sees Arsenal drop back out of the top four, overtaken by North London rivals Tottenham who breezed past relegation candidates Southampton with a 3-1 win.
The former PSG boss was encouraged by his side’s performance though. He told reporters: "I am very proud for our work and how we responded in the 90 minutes.
“When we are winning it was a good moment but they equalised very quickly then we got up after their two goals.
"In the second half our players worked to find a way to win. I think we were close, more than them, to do the third goal but De Gea saved two or three times with good action."
Arsenal are now 20 games unbeaten in all competitions, their last defeat coming to Chelsea on the second day of the Premier League season.
A close eye will be on the condition of Aaron Ramsey who picked up a knock last night, and on Rob Holding whose knee injury looks more serious.
The Gunners welcome Huddersfield to the Emirates on Saturday. A win could see them reclaim their place in the top four if either Tottenham or Chelsea drop points in their games.
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