Ramsey is now set to link up with the Bianconeri on a lucrative long-term contract once his current deal at Emirates Stadium expires over the summer.
Questions have been asked of Arsenal throughout a long-running saga, with this far from the first time that the club have found themselves having to contend with the threat of losing a prized asset for nothing.
Wright believes former manager Wenger, who left north London at the end of last season, must take some responsibility as it was the job of the Frenchman and ex-chief executive Ivan Gazidis to ensure that key men were not allowed to slip the net.
The Gunners icon said “What is really, majorly baffling is that Ivan Gazidis can get another job in the same position. That frightens me.
“I can’t see how AC Milan can look at the way that Arsenal have been mismanaged under his guidance and think ‘yeah, this is the guy for us.’
“I think Arsene Wenger has to take a little bit of blame for the way it’s been managed as well, he’s got to get in with Gazidis and say ‘this guy needs to be signed up now’. I don’t know why his eye was taken off the ball as well.
“Gazidis, that’s his job. He’s got to recognise that this guy is an asset.”
Ramsey has agreed a four-year deal at Juventus which will earn him €7 million (£6m/$8m) plus bonuses per year.
Arsenal had been reluctant to meet the demands of the 28-year-old having previously been forced to dig deep in order to tie Mesut Ozil to fresh terms in February 2018.
Having sanctioned that extension, questions are now being asked of the German playmaker as speculation builds regarding a possible summer switch for the World Cup winner.