Snodgrass is now hoping that Norwich can take something from their remaining two games against Chelsea and Arsenal to secure their place in the top flight for another campaign.
"There is a massive amount of pressure that goes on, each day, as an individual, to give everything you have got," the Scot is quoted as saying by Sky Sports News.
"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."
Norwich continue their Premier League campaign on Saturday with a trip to Chelsea.