Irish fell to a 15th defeat of the league season against Sale on Saturday to leave them four points adrift at the bottom with three games left.
Back row Narraway dismissed concerns at the spirit of his squad heading into the Premiership run-in.
"It's the one thing I think we have in abundance, accuracy and being clinical are things we haven't," he said.
"That's why we find ourselves here (at the bottom)," Narraway added. "Not because of the spirit or the want or desire not being there.
"It's just that 5-10% in terms of accuracy that probably a little bit of confidence gives us," the 32-year-old former Gloucester, Perpignan and England player said.
Irish face Harlequins in the quarter-finals of the European Challenge Cup at The Stoop on Saturday before their Premiership status will be determined in remaining games against Newcastle, Quins and Wasps.
The fixture against fellow strugglers Newcastle at Kingston Park on 17 April has been described as "a Grand Final" by Narraway, who said: "Newcastle is huge, they're one place above us, one win above us."

Taylor, 26, made her debut keeping wicket for Northern Districts in the West End Premier Cricket Competition against Port Adelaide Magpies.
The two-day event is the highest level of cricket played in South Australia outside first-class cricket.
"I am completely proud of what I have achieved today," Taylor told the BBC World Service's Sportsworld programme.
"I would like to think I am not going to be the last woman to play in men's A grade.
"To be the first was never a plan of mine, it has just happened that way. I have to thank the Jets for letting me have that chance.
"It was a long day, it was tough, but overall I was pretty happy with my performance."
Former Australia Test cricketers Darren Lehmann, who is the current coach of the men's national team, and Ryan Harris have previously represented Northern Districts in the West End Premier Cricket Competition.
The second day of the two-day match will be next Saturday, when Taylor will bat.
"It has been a rollercoaster for me and them these past few days, but the guys were brilliant about it," she added.
"There was pressure internally, rather than worrying about external factors, but I am happy with what I have done."
Taylor, who has played in men's league cricket in England, is also playing 50-over state cricket for South Australia in the Women's National Cricket League, and will feature for Adelaide Strikers in the inaugural Women's Big Bash League, a Twenty20 competition.
"One day there might be a girl who comes through and doesn't want to play women's cricket, and wants to see how far she can go in the men's game," said Taylor.
"For me personally, it was just to make a me a better women's player."
Earlier this year, England seam bowler Kate Cross became the first woman to play in the 123-year-old Central Lancashire League.

The Abominable Bride - which starred Benedict Cumberbatch and Martin Freeman as Sherlock Holmes and Dr Watson - attracted 34.7% of the TV audience.
The final episode of ITV drama Downton Abbey won the Christmas Day ratings battle with an average of 6.6m viewers.
BBC One's New Year's Eve fireworks was watched by more than 12m, the BBC said.
Sherlock attracted 8.4m viewers, the highest overnight audience across all channels for a drama of the festive season, the BBC said.
The two-hour Downton Abbey finale attracted a peak audience of 7.1m, beating the Strictly Come Dancing Christmas special as the most watched Christmas Day show.
The Strictly special was the BBC's most-watched show of Christmas Day, with a peak of seven million viewers and an average of 6.5m.

Twenty tonnes of pasta covered the A5 near Shotatton, forcing police to close the road between the A483 at Oswestry and the A458 at Shrewsbury.
A spokeswoman for West Mercia Police, which attended just after 11:30 BST, said it was not clear how the pasta had ended up on the road.
No-one was arrested and no-one was injured.
A Highways England spokesman said: "We sent people there with high pressure hoses to clean it up but it does seem that it got everywhere.
"All of it has needed sucking up and taking away.
"It's been quite a clean-up job."
London Irish captain Luke Narraway says improving their accuracy is the missing piece to their Premiership survival.
[NEXT_CONCEPT]
England's Sarah Taylor made history on Saturday by becoming the first woman to play Australian first-grade cricket.
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BBC One show Sherlock attracted more than eight million viewers for its New Year's Day special - the highest TV drama audience of the festive season.
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A major road in Shropshire was closed after a lorry shed its load of pre-made spaghetti bolognese.