Norrie left his post this week after only eight games in charge.
A statement issued by the West Lancashire League champions on
Monday said: "The appointment wasn't working out in the interests of George or, in particular, in the best interests of Garstang FC.
"We would like to thank George for his efforts during his short time with us and wish him well for the future.''
The decision is understood to have been taken by the club's committee on Sunday, following Garstang's 2-0 defeat at Vickerstown on Saturday, although The Courier understands the decision to let Norrie go was not necessarily down to on-field results.
Dave Porter has been appointed caretaker manager and was taking training this week. He will be in charge for Saturday's Lancashire Amateur Shield second-round tie against Crookland Casuals.
Norrie was appointed in the summer after the resignation of Gary Hargreaves and Scott Somerside, who guided Garstang to the premier league title in their debut season in the West Lancs League.
Norrie, an experienced non-league coach, his previous clubs including Lancaster City, Morecambe, Gretna and latterly Carnforth Rangers and Trimpell, had immediate success as Garstang lifted the Wilf Carr Memorial trophy in his first competitive game, and went on to a first-day draw against Charnock Richard then victory at last season's runners-up Blackpool Wren Rovers.
But it is believed the decision was about the club's vision for the future and Norrie was not considered part of that long-term plan. A club announcement about a successor should be made 'within 10 days'.