The slender victory, thanks to a 86th-minute goal from Lyndon Dykes, puts Scotland on the brink of finishing second in Group F with two rounds of fixtures remaining. They face Moldova on November 12 before welcoming Denmark - who have already secured top spot and a place at Qatar 2022 - at Hampden three days later, but a win in Chisinau would secure a play-off spot next March, most likely as a seed, and render the clash with the Danes largely redundant.
Only third-placed Israel, who Scotland defeated 3-2 last Saturday, can now catch the Scots, who have a four-point advantage over them. The Israelis overcame Moldova 2-1 in Be'er Sheva to keep the heat on Scotland, emphasising the importance of Steve Clarke's men winning in Torshavn.
Scotland were not at their best and had to rely on a big first-half save from goalkeeper Craig Gordon, and Robertson was glad just to leave the North Atlantic archipelago with three points.
"It's a massive win," said Robertson. "It'll turn out to be a huge three points. Probably the less said about the performance, the better. We weren't at our best. First half, we were poor, they won every second ball. We needed Craigy ... what a save he's made. It could have been a lot different.
"Look, when you come to these places, people just expect you to get easy points, but you saw Austria only won 2-0 and the goals were late, Denmark scored in the 85th minute, so we knew it was going to be tough. The astroturf pitch, which none of us are really used to. They are physical., strong, and played their gameplan really well, and we didn't play exactly how we wanted to. The confidence they get from winning second balls, beating you to the ball, getting a chance and their fans lifted them. We had to dig deep.
"But six points at the start of this week was crucial and now we are close to what we achieved and it's important to keep that in mind.”
Speaking to Sky Sports, Robertson added: "Saturday was a really emotional game and maybe the lads had a wee hangover from that. But when games are like that, it's so important to get through. We could easily be standing here talking about a 0-0 and how November would be a lot, lot harder.
"I'm glad we got there in the end but we need to be a lot better than that going forward."