The combative midfielder has stated that the main reason for his departure was because the Rossoneri trainer felt he would be more useful as part of the coaching staffAC Milan this summer because head coach Massimiliano Allegri "no longer needed" the duo.
The holding midfielder exited the Serie A giants for Sion after a 13-year spell with the Rossoneri, while Nesta joined Montreal Impact after 10 years at the San Siro side.
"The reason why Nesta and I left is because we got the feeling that we were no longer needed by Allegri," Gattuso stated to La Gazzetta dello Sport.
"When someone like the coach makes it clear to you that he prefers you as a coach or as a helping hand in the dressing room, the time has come to leave.
"I don't hold any grudges, though. I'm proud of my time at the club. They wanted to hold on to me, but it's difficult when those in command of the changing room think different.
"There's no controversy. I have a good relationship with Max [Allegri]. It's just that I still feel like a player."
Gattuso made his official Sion debut at the weekend in a win over Grasshoppers, and was shown a yellow card before leaving the pitch with a minor muscular problem.