Unai Emery’s side twice took the lead at Old Trafford but were pegged back and had to settle for a point.
Shkodran Mustafi opened the scoring as David De Gea made an uncharacteristic error in the Manchester United goal.
But moments later Anthony Martial levelled to make it 1-1 at half-time.
Marcos Rojo was attributed with an own goal in the second half to give the Gunners the lead but Jesse Lingard equalised seconds after.
And Mkhitaryan revealed Arsenal felt frustrated at the result.
He said: “There is a lot of frustration because we should have won.
“I think we deserved to win but we drew. We were trying to score the third goal but unfortunately, we couldn’t.
“Even if you have tired legs, the most important thing is to be fresh in the brain, in the mind.
“If you force yourself, if you push yourself to get to the end, then you will do that.
“You don’t have to listen to your legs, even if they are heavy or it’s hard to play.
“You have to do the maximum.”
The result leaves Arsenal in fifth place level on 31 points with Chelsea.
Tottenham are two points clear in third with leaders Manchester City 10 points ahead of the Gunners.
Emery’s side return to action against Huddersfield at the Emirates on Saturday (3pm).
Arsenal will look to get back to winning ways with a dominant performance against the Terriers.