Walker spoke about his anxiety at informing Pep Guardiola of his decision to leave Manchester City.
The 34-year-old England defender was unveiled by Milan this week, citing a lack of playing time as a key reason for his loan move.
Guardiola's response to the situation has been terse, stating that Walker "decided to leave."
On going to Milan, Walker said: “When I spoke with Pep, it wasn’t a comfortable conversation because of the respect we have for each other.
“What he’s won at City, I have won it, too. I like to think he knows what I bring to a dressing room.
“City was my family — from the cooks to cleaners, kitmen and physios. I like to think I was liked and helped everyone blend in.
“But things weren’t going well there and I wasn’t playing enough.”