Ferguson said: "Mikael Silvestre came to see me at the end of the season and said he wanted first team football. I agreed with him.
"He has given me nine years good service. There is no point in holding onto a player who has lost his position to Patrice Evra.
"He was conducting his own affairs. We knew the price we wanted and notified the clubs who were showing interest.
"Mainly it was Sunderland. He went there last Friday to discuss a move and he came back and was very positive about that.
"Then Man City came on the scene.
He was having a medical there and halfway through it he got a phone call to go to London and he ended up at Arsenal."
Brian Kidd was the last United player to move to Arsenal when he made the switch in 1974.
Ferguson added: "We have no complaints. We wish him well.
"You could have been selfish and say you are going to be a reserve. But we are bigger than that.
"We recognised the service and let him get on with a career playing first team football."