The hosts went ahead early on when Theo Walcott fired past David de Gea, but former Gunner Robin van Persie earned the Red Devils a point from the penalty spot after Bacary Sagna brought him down in the box.
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"We had the best chances of the match, we had four fantastic headers," he told Sky Sports. "In the last third if we had had more composure we would have won the game.
"The game was end to end, particularly the last 20 minutes, but the best chances definitely fell to us and maybe we should have done better.
"We expected a tough game, but I think in fairness to our players, if we’d have taken one or two of our chances in the first half we would have won comfortably."
The Scot was also unhappy that his side received five yellow cards over the course of the afternoon, suggesting referee Phil Dowd struggled to keep up with the pace of the game.
"I think Arsenal set off at a fantastic pace, they were very aggressive," he added. "I think the referee couldn’t keep up and then when we had a foul we got booked straight away.
"Five bookings, we had the best disciplinary record in the division so to get five players booked I don’t think that’s right."