The Scotland midfielder was a frustrated onlooker for the loss to Luton as the Canaries became the first team in the Premier League era to exit the FA Cup to non-league opposition last Saturday.
But Snodgrass was involved in the previous week's 5-0 loss at Liverpool which means Norwich have one point from 18 entering Wednesday night's Barclays Premier League clash with Tottenham, who lost their FA Cup fourth-round clash to Leeds.
The 25-year-old, who has been a key player for a Norwich side which had a 10-game unbeaten run earlier this season, said: "Seasons are full of ups and downs. We're going through that stage just now that most teams go through.
"You need to show character. I've said that word 'belief' many times, because it takes that.
"We've got a great squad of boys and you need to dig deep at times like this, hopefully grind out a few results and pick ourselves back up."
The midweek arrival of Spurs to Carrow Road is welcome, following the reverse to the Hatters.
"It's a great time to have a midweek game and hopefully we can get back to winning ways," Snodgrass added.
"We've already beaten Spurs at home (in the Capital One Cup). We ran them close down there at White Hart Lane (drawing 1-1).
"It will be a tough task, but I believe we've got the character, strength, depth, the full lot in the squad that we can go and do it."
Snodgrass' former club Leeds ended Spurs' FA Cup run this term, but he recognises the quality Andre Villas-Boas' side possess.
Yet he maintains Norwich can claim victory over Spurs for the second time this term and pointed to scalps his side have already claimed at home, notably Arsenal and Manchester United.
"They're still fourth in the Premier League," Snodgrass said.
"They're in the Champions League spot in the Premier League not by luck, they're there by the quality they've got in the team.
"But on our day, especially at Carrow Road at times, we've put in some great performances.
"The manager will drum that into us and let us know that those games are finished with, you can't change what happened in the past.
"I believe in the squad that we've got, that things will be fine."
Norwich boss Chris Hughton is eager to add to his squad before Thursday's closure of the transfer window, with a striker a priority. Celtic's Gary Hooper is among the players linked.
Asked if he has used his Scottish connections in an effort to influence the deal, Snodgrass said: "No. I'd have about 50,000 Celtic fans wanting to rip my head off."
If a deal can be struck and if Hooper does move to Carrow Road, he would forgo the opportunity to play in the Champions League last 16 for Celtic against Juventus.
Snodgrass would not be drawn on that decision, but believes any new signing would feel at home.
"He (Hooper) is doing well," Snodgrass said.
"He's a good footballer. If it happens, it happens. I know it would be a good addition to the squad.
"It's quite easy if there is any signing coming in. We've got a great bunch of lads here and they'll settle in really well."
Snodgrass is among the players poised to return following the Luton defeat.
Defender Sebastien Bassong has recovered from a calf injury and Steven Whittaker is fit again following a hip problem.
Steve Morison (thigh) could be available for the weekend match with QPR, but England goalkeeper John Ruddy (thigh) remains out.