The former midfielder clocked up an impressive 433 appearances during his time at Goodison Park, scoring 57 goals along the way, as he became a stalwart on Merseyside.
Osman told The Sportsman: "That's [a text] how I found out I was no longer going to be at the club, so I suppose when you say that, it's a bit disappointing.
"The discussion was to be had, Roberto told me that I'd still be at the club the following season but then he lost his job before the end of the season.
"I seemed to fall in the gap of the uncertainty over who the new manager was going to be. It's disappointing, these things happen.
"I would have liked to have had a nice match at Goodison to say my goodbyes, myself and Tony Hibbert who was in the same situation. We just didn't happen to get that.
"Time is the healer of most things. I wouldn't say I'm completely healed, it'll always niggle in the back of my mind, the way it happened."