United stunned the Premier League leaders 3-2, with Matheus Cunha scoring the winner three minutes from fulltime.
Dixon told BBC Sport: "That is the sloppiest I have seen Arsenal in a long time.
"It was a disappointing performance. I think they were in control for the first half an hour, but they were not creating anything, which has been a problem of late.
"They just looked a little bit off the pace. They did look under pressure when Manchester United started to come back into the game a little bit and that mistake can tip you over the edge.
"I think Mikel Arteta came out, and he said he was going to stick to the players, which he should do.
"People tell you that you don't go through a season and win a league and get it all your own way.
"This is Arsenal's time just now, and it is how they react and how they bounce back in the next game."