The Canaries play Chelsea and Arsenal in their final two fixtures but the winger insists they can still save themselves and refuses to concede they are doomed to relegation
A run of six defeats in seven Premier League matches has seen Norwich slip into the bottom three, with their latest setback a 4-0 loss at Manchester United on Saturday.
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But winger Snodgrass is hopeful he and his team-mates can raise their game, despite the heightened tension at Carrow Road.
Speaking to Sky Sports, he said: "There is a massive amount of pressure that goes on, each day, as an individual, to give everything you have got.
"You need to better yourself every day to give yourself the best possible chance to stay in this division.
"It doesn't get any easier, playing against the likes of Manchester United, Chelsea, Arsenal, but it's what you want to be in the Premier League for, to play against the best.
"We'll roll our sleeves up and try to give a good account of ourselves and get a few results."