Nevin, himself, was pushed out by the club during the season from his media duties.
He told BBC Sport: "Not in the slightest (am I surprised). I think he did a good job with what he was handed. By the last six or seven games it looked like he had done the job.
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"Doing it any quicker would have bordered on impossible. There were noises coming from Pochettino that he would like more control in certain areas, but I don't think he gets that option, that comes from elsewhere.
"A number of things have changed how he sees that role, and it doesn't suit either party any more."