Nicolas Pepe and Sokratis scored for the Gunners, as they climbed into the top half of the table.
The result however sees United five points adrift of top four places and Maguire, speaking to MUTV afterwards, said they were a long way off the pace.
“We started the game well. In the first 10 minutes we created two good opportunities where we should have been a little bit more clinical. And then from there until the half-time whistle they were on top.
“They played with more aggression, more intensity and they pressed us better. So we’ve got to go back, work hard, improve.
“In the second half, we huffed and puffed and created some chances, but the key period was from the 15th minute until the half-time whistle and we weren’t good enough,” Maguire said.