With the club still in danger of being relegated, the Norwich board decided to sack Chris Hughton and replace him with youth team coach Neil Adams, who will be in charge of the team for the first time in west London.
A victory over a Fulham side in the drop zone would boost Norwich's chances of survival and Snodgrass has urged his team-mates to give their all as they look to retain their Premier League status.
"It is a battle of who wants it most, who wants to keep their club in the Premier League. I'm relishing it, I can't wait," said Snodgrass.
"It's now or never to try to get a result. It doesn't come any bigger than this.
"They'll come out all guns blazing. I don't care what way the game is (played), just give every single thing you've got. It's time for characters, leaders, everything you've possibly got.
"It's a time for heroes. I want to be that person. I want to be the person that keeps Norwich in the Premier League.
"I want to be part of that. I don't want to be part of a side that gets relegated."
Norwich face an extremely tough run-in after their trip to Fulham, with a home game against Liverpool followed by away games against Manchester United and Chelsea.
They conclude their campaign by entertaining Arsenal on the final day of the season and, with the emphasis on picking up something from the Fulham fixture, Snodgrass is keen for the team to immediately get behind Adams.
"Hopefully we can get the new manager off to a winning start on Saturday," he added.
"He's got Norwich in his blood. He knows exactly what it means to the fans and that's what we should all think about, what it means to this city.
"What it means for this club staying in the Premier League and for us, as players, as well.
"Some of us might never get that chance again to play there (in the Premier League)."