The Leeds academy product even earned an England call-up during the recent international break, but was an unused substitute against Brazil during the Three Lions' 0-0 draw.
Redfearn, who nurtured Cook through the Elland Road academy system at Thorp Arch before managing the youngster at senior Leeds level, believes the Whites would be a better side if they had kept Cook.
The 52-year-old former boss also considered Cook's England chances after his call-up, claiming he will be given a second bite at the cherry to shine for Gareth Southgate's side.
"He's a fantastic talent," Redfearn said. "The lad has moved on whatever reason, but it is a shame for Leeds because I think if Leeds could have kept hold of a player such as Lewis Cook, for me, that was the way forward.
"These are quality players, and quality people. They've been brought up the right way. I think his chance will come [for England], if you look at Dom Solanke who came on, Cook has played quite a few Premier League games now.
"I think his chance will come."
Cook managed 85 appearances for the Whites in all competitions after making his Leeds debut in August 2014 under Dave Hockaday, before being sold two years later.
The youngster's defining moment of his short career is likely to be holding aloft the Under-20's World Cup trophy in South Korea this summer, after captaining Paul Simpson's side to success.