Gunners manager Arsene Wenger insisted Darron Gibson should've been sent off during the stalemate.
Moyes defended his side's approach.
He said: "Do you mean when we were a little bit rough with the tackling? Up north we do that quite often, that's actually allowed in football.
"We weren't going to come here and let Arsenal stroke the ball around and make 600 tackles."
Moyes added: "I am pleased with the performance, and with the result. You are never disappointed taking a point at the Emirates, you can't be with the quality they have here.
"We went to try and win it. We knew if we got three points here we would have a real chance (of the top four), but a point keeps us ticking along."