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.
Norwich's survival prospects look bleak given their remaining games are against Chelsea and Arsenal.
However, 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."
‘I joined Salford, initially on loan, from Derby U21s – I may be the only manager who’s ever gone out on loan! I loved the history and where the club came from’: Football League boss recalls bizarre managerial move in 2021
'They said I fought with Mario Balotelli at Swansea and against Sunderland. That shocked me. My lawyers called me about this, and it was the first I knew about it. It upset me, and I feel sorry for Mario.' Yaya Toure clears up Manchester City fight talk
