The Lanarkshire outfit lost to goals from the Scotland Under-20 centre-half Cameron Burgess and Chris David either side of the break against a visiting side that fielded their recent £11m signing from Leeds United, Ross McCormack, and the former Motherwell defender Shaun Hutchinson.
McCall admits his team have a historic weakness against European opposition capable of attacking at speed on the break and, having travelled to Wales to watch their four-goal win over Bangor City last week, he believes Stjarnan are more than capable of posing problems in that regard.
He sees their 34-year-old striker Veigar Pall Gunnarsson, with 33 caps for Iceland under his belt, and fellow forward, Arnar Mar Bjorgvinsson, as the major dangers and has ordered his players to tighten up ahead of Thursday's second qualifying round, first leg home tie.
"I'm not making excuses in case things don't go right, but they have two or three really talented players and you only need one or two who can change things," stated McCall.
"There were times against Fulham when we were on top and going forward, the ball broke and Ross McCormack, just playing off the front, was two against two.
"In every European game at Fir Park, we've been caught on the break when we've been on top, so we have to wary of that.
"They have capable players who can break from the middle of the park and in wide areas.
"They have wide players who can score goals and a couple of experienced boys in the middle who can make passes.
"The lads will be well up to speed on them, though. We'll watch clips and they'll know all about them.
"We'll be ready. They have capable players, but so have we. We're hopeful we can cause them problems and have identified a couple of areas where I hope we can get at them."
In addition to scoring eight goals in two legs against Bangor City, Stjarnan are second in the Icelandic League with a game in hand, having played 10 fixtures, and could go top later today should they beat current leaders FH Hafnarfjordur at home.
"They are halfway through their season and they are fit and strong, but our lads have worked hard since they came back and the crowd getting behind us on Thursday night will help get us up," stated McCall.
The manager is desperately seeking a centre-forward in addition to a centre-half, but has revealed he will not be offering a contract to striker David Clarkson, who spent time on trial at his former club last week.
"David is no longer with us," he revealed. "I had a little chat with him on Friday. He trained well and he is a decent lad, but he is not exactly what we are looking for. We are looking for a little pace to go in beyond and we looked at him playing a slightly different position.
"I have watched a lot of games from last season and you will remember Henri Anier running away and scoring on the first day. I don't think we have that in the side at the moment and we are looking for someone like an Anier or a Henrik Ojamaa that can use pace to get in behind."
Motherwell struggled to create clear-cut chances against Fulham and went a goal behind on 20 minutes when Burgess was allowed to connect with a David corner and head home from an unmarked position.
Keith Lasley did see a 36th-minute shot deflected wide by Hutchinson before a dreadful error by Dan Twardzik allowed the visitors to go two in front. David released a speculative 25-yard shot that the goalkeeper failed to stop from bouncing over the line despite getting both hands to the ball.
"They are a big side, but we were disappointed to lose a goal from a corner kick and the second one was an individual error," said McCall.
Zaine Francis-Angol was also forced to go off injured just nine minutes after replacing Lionel Ainsworth at half-time and is a doubt for Thursday.
"We thought Zaine's knee had locked, but it turns out it is coming from his hamstring and he had ice on it after the game," said McCall.
"He doesn't think it is too bad. His knee joint is certainly fine. It is just the little tendon in behind it, so we will have to monitor that."
McCormack, a former Motherwell player, was the centre of attention following his midweek transfer and did force one late save from Twardzik. The Fulham manager, Felix Magath, believes McCormack, with just 11 caps for his country, can make himself a Scotland regular by performing well at Craven Cottage.
"He has a lack of fitness at the moment and he was not able to show everybody just how good a player he is, but I'm very confident that he is the right player for us," said Magath.
"I hope first that Ross will score more goals for us than he did at Leeds last season. If he does, I am sure Gordon Strachan will keep his eye on him."