Within the walls of Fir Park, though, there remains a burning sense of injustice.
Stuart McCall's side had been instructed in some detail, as a result of past disasters suffered in UEFA competition, to be wary of being hit on the break by their Icelandic opponents in the first leg of their Europa League second qualifying round tie.
Within four minutes, they had allowed their concentration to slip, escaping thanks only to Veigar Pall Gunnarsson, Stjarnan's veteran forward, who missed a clear header from a matter of yards after being permitted to start and then finish a sweeping move.
Despite the fact Motherwell were to go two goals up within 19 minutes thanks to Josh Law, making his debut in claret and amber, the home side remained incapable of strangling the life out of the fixture and making a third qualifying round encounter with the Estonians JK Nomme Kalju or Lech Poznan of Poland a relative formality.
A penalty conceded 10 minutes before the interval changed the face of the game. Stjarnan carved out a number of openings and scored their second goal from the spot in stoppage-time after a bout of bagatelle in the goalmouth ended with Keith Lasley, guilty of handball in his own area earlier on, pulling the shirt of Ralf Toft.
By that stage, Motherwell should probably have settled for taking a 2-1 lead to the part-timers' plastic pitch in Gardabaer. Instead, they kept pushing for a third goal and Law believes that approach ought to have brought its reward when Simon Ramsden went down in the box amid a ruck of bodies in the dying moments and claimed immediately for a spot-kick of his own.
"We feel very hard done by," said Law. "Maybe they were penalties for them but, before their second one, we feel Rammers got tugged back. The lad took his legs away and they have gone straight up the park and got themselves a penalty. There is no reason why we can't go over there and win. We just need to tighten up a little.
"Obviously, I'm delighted to get my first couple of goals for the club, but it really counts for nothing as the game was drawn. The start we got was perfect. That should have led to them coming on to us and leaving us to counter, but it went the other way and we left big holes."
One man who was happy to expose those was Ola Finsen. The attacking midfielder converted both penalties and really should have scored another goal on 57 minutes only to volley wide from six yards.
Tall and direct, Finsen looked the kind of player that could do a job for a side performing a higher level. He certainly believes Stjarnan are capable of doing a job on Motherwell in the return leg. "Yes, I think so," said Finsen when asked if his team is confident of victory in Iceland.
"I think we are in better shape. We are on a good run and there is confidence throughout our team. No-one seems to enjoy playing on our pitch and I hope that continues next week.
"In Iceland, we use artificial pitches all year, but still you find all the teams complaining. Other countries have artificial pitches in the top division. We will make it as hard for Motherwell as we can."
Law realises an artificial surface is likely to cause some additional headaches in what is already shaping up to be a difficult tie against a side that is sitting second in the Iceland Urvalsdeild after 11 matches. Stjarnan also remain unbeaten so far this season.
However, the midfielder does not expect it to prove a defining factor in the match. "We have heard it's a really good pitch," said Law. "We know it's not grass, but we've played on similar surfaces before. They are well into their season and Thursday night, for a lot of us, was our first 90 minutes [since last season]. Fitness definitely played a part towards the end, certainly in the last 20 minutes. They looked fitter and we looked leggy."
Finsen returned home more than happy with his own shift. He believes the 2-2 draw at Fir Park may well be Stjarnan's finest achievement, but he realises real history can be made next week in what is the club first excursion into European football.
'Where does this result rank in Stjarnan's history? Number one," he said. "I don't know the history too well, but why shouldn't it be the best?
"Motherwell played as we expected. We could have scored first and that could have made it a different game."