St Mirren kept their hopes of Conference League qualification alive despite a hugely frustrating night in Reykjavik.
The visitors passed up multiple gilt-edged chances to take a lead back to Paisley for the second leg next week.
Toyosi Olusanya saw numerous first-half chances pass him by as St Mirren were unable to hit the target with a handful of opportunities.
Valur had chances of their own forcing Ellery Balcombe into top stops to keep the tie goalless.
The hosts were reduced to ten men as St Mirren pushed for an opener late on when Aron Johansson threw himself into a tackle on Jonah Ayunga. But the visitors could not make the most of their numerical advantage in the final ten minutes.
Olusanya sums it up
Toyosi Olusanya's display in Reykjavik was the perfect microcosm of St Mirren's performance as a whole.
A powerful striker with pace to burn, Olusanya caused Valur problems all evening but, crucially, could not find a killer touch.
Countless opportunities were spurned by the forward and his team-mates in a hugely frustrating night in Iceland.
It's never for lack of effort but simply composure that let down Olusanya and St Mirren. There were moments of brilliance and tireless running but simply no end product.
An early opening was thwarted by a smart stop from Frederik Schram and minutes later Olusanya - perhaps with that miss in the back of his mind - harmlessly squared to a defender with the goal at his mercy.
It wasn't just Olusanya culpable for missed chances, though, Mika Mandron saw a prodded effort drift inches wide with Schram beaten while Oisin Smyth and Dennis Adeniran saw wayward strikes fly well clear of the crossbar.
Sub Roland Idowu had an impact with his directness but even he couldn't find an all-important opener as a low drive was parried clear.
Sloppy Saints
In Europe there is little margin for error. St Mirren were hapless in front of goal and as the match wore on sloppiness began to creep into their game.
Hosts Valur are 14 games into their domestic season while this was the first competitive outing for Stephen Robinson's side after four pre-season tests.
Perhaps match sharpness played a factor as Valur only truly threatened when presented with the ball in dangerous positions by St Mirren players.
Questionable clearances, ropey outballs and more than a few unforced errors saw the pressure ramp up on occasion for St Mirren with the hosts threatening a suckerpunch.
It was unusually sloppy for a Robinson side on a big occasion. Fortunately, Ellery Balcombe was on form as a final line of defence.
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Brilliant Balcombe
St Mirren had goalkeeper Balcombe to thank on a number of occasions as he spared blushes in Reykjavik.
The on-loan Brentford stopper earned huge plaudits in pre-season for his distribution but it was his goalkeeping fundamentals which caught the eye.
Within two minutes he was called into action to deny Jonatan Ingi Jonsson who had found space at the back post. Balcombe was quick off his line and prevented an opening goal as the ball struck him on the face and clear of danger.
Tryggvi Hrafn Haraldsson had a sighter after 12 minutes but Balcombe saved smartly as the shot squirmed through the legs of Elvis Bwomono.
In the second half Balcombe was kept just as busy. Six minutes after the restart Patrick Pedersen burst into the box from a quick throw and rounded Alex Gogic but Balcombe again played the hero for the Paisley club.
A strong Haraldsson header looked destined for the net after the hour but for the incredible diving stop of Balcombe who used every inch of his frame to keep his side level.
Gylfi Sigurdson would then test him again with a stinging drive forcing Balcombe to tip over.
Valur no mugs
For all the focus on St Mirren, hosts Valur played their part in the stalemate and proved they're not to be taken lightly.
While St Mirren boast quality which should see them through should chances be taken - there is some top players plying their trade for their Icelandic opposition.
Jonsson was a constant threat as one of Valur's top performers this season. Sigurdsson still possesses quality that allowed him to become a Premier League player while a little off the boil at stages.
And in Haraldsson, there is a danger man St Mirren must contain next week if they're to progress in the competition.
History makers
Robinson and his charges made themselves history makers with a first appearance in Europe for St Mirren in 37 years.
A special occasion was lapped up by the strong travelling support who took over Reykjavik from days before the Conference League fixture.
In the stands, there were St Mirren legends too with Tony Fitzpatrick, David Winnie and Gunni Torfason backing the Buddies.
Now Fram chairman, Torfason was surrounded by fans with a hero's welcome on his arrival at the stadium. Fitzpatrick - who was roundly mocked for his belief in St Mirren returning to the European scene - embraced the tie watching training on Wednesday before kicking every ball at the Hildarendi Stadium.
St Mirren players might have written a new chapter in the club's history with their appearance in Europe but one record still standing is Kenny McDowall's claim as the last Paisley player to score in continental competition.
Fans, players and staff alike will be hoping that changes come next Thursday.
ST MIRREN XI: Balcombe, Taylor, O'Hara, Smyth, Mandron, Gogic, Boyd-Munce, Olusanya, Brown, Fraser, Bwomono.
SUBS: Urminsky, S. Kelly, Tanser, Ayunga, Idowu, Scott, Adeniran, Jamieson, L. Kenny, Taylor, Mooney, Sutherland.
VALUR XI: Schram, Gunnarsson, Helgason, Antonsson, Jonsson, Pedersen, Sigurdsson, Larusson, Haraldsson, Palsson, Sigurdsson.
SUBS: Agustsson, Kristinsson, Saevarsson, Johannsson, Tryggvason, Eyjolfsson, Unnarsson, Heimisson, Omarsson, Stephensen, Finsen.
