Sheedy coached his 679th and final game at Metricon Stadium on Sunday, and Matthews said his contribution would never be forgotten despite seeing the Giants lose by 83 points.
He described Sheedy as "the father of the Giants" and said no other coach could have put them on the map in western Sydney like he had.
Sheedy won three premierships as a player, four as a coach, helped establish games like Anzac Day and Dreamtime at the 'G, but Matthews says the risk he took by coaching the Giants should never be underestimated.
"He could easily have sat in Melbourne and enjoyed his unbelievable career," Matthews said.
"He's been the cornerstone of this club and the father of the Giants in many ways.
"I don't think there was anyone else who could have done the job he's done.
"I think his legacy was assured before he came up, but I'm hoping in many ways this will be the biggest part of his legacy.
"In many ways this is the hardest thing anyone's tried to do in the game. I can't imagine anyone who could have done it."
Sheedy has not decided on what he will do next year, but Matthews said he would encourage him to stay involved at the Giants.
"The club is still incomplete in many ways and no doubt the foundations have been laid (by Sheedy)," he said.
In his final post-match press conference, Sheedy mixed his usual quirkiness with insightfulness and perspective on the early Giants journey.
He said he left the game content and got just as much satisfaction out of giving young players opportunities as anything else.
Sheedy also left no-one in any doubt how much time he put into the game, giving one final insight to the entertainer in him.
"I'm always arguing with my left brain. We get into heavy debates in front of your own mirror. How deep do you want to go today ladies and gentlemen?" he asked to much laughter.
"When you stuff up, you stuff up - I've done that over the years, but in general a lot of people lack the courage to be creative and that's a sad thing. I hope I've never done that."
Twitter: @AFL_mikewhiting
