Wenger is a big fan of Southgate, recently calling the former Boro skipper one of the bright prospect in the English game, and warning that the Teesside club could be a major force next season.
Southgate may have been the first manager to taste victory over Wenger this season, but despite his success over Arsenal he is stunned by the reaction to their European exit this week.
He said: "I'm staggered by it really. If any of us had sat here at the start of the season with Henry gone, I don't think many would have predicted they would have been close to top of championship or three minutes away from the semi-final of the Champions League.
"There are narrow margins in football, but I find it amazing that people can say he hasn't bought enough players, or assembled a big enough squad.
"I'm sure they've gone further than even he thought they might, although I'm also sure he wouldn't say it publicly. It's funny, people have a fantastic time and achieve more than people thought they would and then they get criticised because they've not gone the final yard.
"Manchester United and Arsenal are special because of the way they move the ball, they cause you problems that the other teams don't . They attack at every available opportunity and they're both a joy to watch."