United's second-string are still awaiting their first win of the 2019/20 season following defeats to Reading, West Ham and Manchester United.
And Walters - who plays as a left-back - is targeting a maiden victory against the Cottagers before the young Magpies begin their Leasing.com Trophy campaign at Macclesfield Town on Tuesday night.
"It's a very important game for the team," the 19-year-old told nufc.co.uk. "We need to get off and running and try to get three points on the board to progress up the table.
"A win would mean a lot for the squad and gives us all a lot of confidence going into the next couple of games. Hopefully, we can get off the mark.
"It's a big week for the team. We've got the game against Fulham but also have to play Macclesfield. If we can get a win against Fulham, it will boost our confidence and we can take that into the next game and try to get a win too to try and progress in the competition like we managed to do last year.
"We are quite a confident group and everyone believes that we are much better than the way we have been performing recently. We know we can get a positive result and kickstart our season.
"We've got a lot of players who played in the team last year. There are a few new lads too but we are trying to get them to gel together in the group and then hopefully we can start picking up some results.
Last term, United defeated their Fulham counterparts on both occasions in Premier League 2, recording a convincing 5-2 victory at Whitley Park before earning a 1-0 win at Motspur Park in March, with Walters appearing in both fixtures.
However, after shipping 12 goals and scoring once in their opening three league meetings, Walters is determined to respond brightly from the difficult start and replicate the form which saw United finish fourth last season, earning 40 league points in the process.
The Newcastle-born youngster added: "We played against Fulham home and away last season and won both games. We can take a lot from that and hopefully do the same when we go down there for tomorrow's game.
"Last year, we also had a slow start. We did very well last year but the slow start at the beginning of the season costs us towards the end. We've been working really hard in training with our defensive work to try and stop conceding goals.
"Neil (Redfearn) has been mentioning 'siege mentality' to stop our opponents from scoring so we'll be wanting to take that into the game and hopefully we can come away with a clean sheet.
"The first game (against Reading) wasn't great but we bounced back against West Ham and we were unlucky not to get three points then so we want to get off to a strong start, try to gain a clean sheet and hopefully come away with three points."
