The Hammers were second best in every department as a rampant Leicester got back to winning ways on Wednesday night, leaving the east Londoners above the drop zone on goal difference alone.
The return of Michail Antonio offered a glimpse of hope that a second half revival was possible following Mark Noble's penalty, but the rampant Foxes ran away with things late on with West Ham chasing shadows.
Snodgrass said: "We have got some tough games coming up so we need to dust ourselves down for this and we need a few home truths and watch the game back, see where we get it right, where we put it right.
"There are still a lot of points to play for but it is not a good enough performance as a team, we know that and we need to watch it again and come back stronger."
That tough run could see things get a lot worse before they improve. The Hammers face Liverpool twice as well as Manchester City across the next month and manager David Moyes is hoping his side can spring a surprise to help them through the run.
"When I was coming into the job I was aware of how tough January would be," said Moyes.
"But, my hope is that the Premier League always throws up surprises and shock results and we have to be looking to make one of those happen."
Moyes has been hampered by injury in his early weeks back at West Ham, having already lost Felipe Anderson for a month as well as goalkeeper Lukasz Fabianski.
Just five minutes into Wednesday’s contest at the King Power, Snodgrass - who has been in fine form of late - suffered a knock to the same knee which has caused him problems in the long term. The Scotsman will undergo a scan on Thursday to assess the damage and - while he feels it is nothing too serious - it is another setback for the Hammers.
"I'm obviously gutted that I got a bang," said Snodgrass. "It is disappointing on a personal level, I've been feeling good and feeling fit and played a lot of games so to get a bang on it, these things happen in football you just need to dust yourself down and get on with it. [I’m] just gutted it has happened."