Nuno was dumped by Forest on Tuesday morning and replaced by former Tottenham manager Ange Postecoglou.
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Reacting to the axing, Keane said: "Not surprised.
"Why should we be surprised at what happens at Nottingham Forest?
"I think we know what the owner is like there, no surprises, and I have no sympathy for any manager either that goes to Nottingham Forest.
"You're going to be under pressure with the owner there, so I certainly wasn't surprised when they moved him on. It's tough."