Norwich spent big in the summer, but they recorded only their second win of the season as they grabbed victory at the Britannia Stadium.
Scottish star Snodgrass is adamant that the club were being harshly criticised before the Stoke win, but now hopes that win will help.
"With performances like that, I don't know how anyone can criticise us. We went to Stoke and won, which not a lot of teams will do," he told the Norwich Evening News.
"The fans are right behind the manager - they're a different class here.
"They felt frustrated that we had so many chances against Aston Villa the previous week and didn't take them, but there's no better way to put things right than to roll your sleeves up and pull off a result like that.
"He has spent maybe £27million on players and the manager will tell you himself that there is an added pressure when you have a bigger kitty to spend.
"We're in the Premier League and there's pressure. I'll be honest and say that if you can't handle that pressure, there's no point in being here.
"In your job, every day, you put pressure on yourself. Even on the training ground, we're putting pressure on ourselves to get better and to work on our weaknesses.
"The manager puts that pressure on us - and the fans put the pressure on the players and the manager. It's not just the manager. We're all in it together."