The ex-Hoops boss was the man who discovered Given and signed him up, only to see the Donegal kid dumped by Celts not long after Brady was fired in September 1993.
Brady told the Scottish Sun: "Shay is one of the best keepers, not just in the English Premiership, but in European football.
"Any club would want his services and I am not surprised so many offered to take him away from Manchester City.
"I knew he had talent as soon as I saw him and that's why I brought him to Celtic.
"To this day, I still can't understand why Celtic let him go after I left. They should have had him tied up for years. Celtic have never had a keeper of Shay's quality in all the time he has been down in England. Certainly not for his sheer consistency.
"It's a pity Shay never got the chance to start his career at Celtic.
"He's a great fan of the club and the fans would have loved him, especially the way he has developed."