The Canaries beat Hull 1-0 on Saturday to record a first win in seven Barclays Premier League matches which moved them five points clear of the relegation zone into 12th place and eased the growing pressure on Hughton.
Despite calls for the former Newcastle and Birmingham boss to be shown the exit door at Carrow Road following a £20million summer spending spree which so far has failed to bring about consistent results, Snodgrass insists the manager can only do so much once the players have gone out on to the pitch.
"It is the players fault - it is not lack of effort, it is putting the ball in the net and that is the only thing that has been lacking," Snodgrass said to the Eastern Daily Press.
"We have got so much determination and we want to do well, but you need to score - that is what wins the game. It is not through lack of chances or trying.
"If we had gone off 0-0 at full-time on Saturday, we would have the fans against us saying we had not done enough."
Norwich lost their FA Cup third-round replay 3-0 at Fulham in what was another abject display from Hughton's men, meaning the next fixture will not now be until Newcastle come to Carrow Road on January 28.
Snodgrass maintains the players will be itching to get back into action.
"You could say it (the break) is handy, but you want to keep playing and keep that momentum going," he said.
"I think the manager would want the games to come thick and fast.
"We will be full of confidence and if we keep showing enthusiasm and take momentum into it, we won't be far off."
Norwich on Tuesday confirmed they had rejected a transfer request from unsettled Ireland midfielder Wes Hoolahan, a reported target for Aston Villa, managed by former Canaries boss Paul Lambert.
Hughton is himself on the lookout for reinforcements, having last week brought in midfielder Jonas Gutierrez on loan from Newcastle and has now been linked with a £2million move for French defender Mickael Ciani from Lazio.
Norwich, meanwhile, are set to subsidise £10 off tickets for the away match at West Ham on February 11.