The defender has now retired from playing and is expected to be named as Millwall's permanent reserve team coach in the coming days. He was tipped to become part of Chris Coleman's backroom staff at the Ricoh Arena but those upstairs had other ideas and scrapped City's reserve team.
Shaw who made 362 appearances for City,played with Coleman at Crystal Palace and told the club website: "Chris will say he carried me all them years but I remember it being the other way around. But he's a fantastic man, people want to play for him and as far as I'm concerned he has been a really good appointment for the club. He'll get things right at Coventry," he said.
"Clubs need a manager there three, four, five years to get things right and in Chris, Coventry have someone capable of that."
Speaking about his time at Coventry and his testimonial versus Celtic, Shaw added: "I was touched with my testimonial and the attendance on the night. I'm not a Robbie Keane who will take on ten blokes and score and I wasn't a Gary McAllister who could spray 85-yard passes but I'd like to think I was a player that gave 100 per cent on the day and that I was reliable because it still means a lot to me what the supporters think.
"That testimonial evening was a fantastic night and probably the best I had in football to be honest.
"I got a fantastic reception when I came to the Ricoh Arena with Millwall to play Coventry in the FA Cup in January so I must have done something right during my time with the club.
"I had some great years at Coventry and loved every moment of it. I always look for their results and probably will do for the next 20 years."