The Fir Park club let slip a two-goal lead, against the side who are unbeaten in their domestic league this term, despite new signing Josh Law scoring a double.
Lasley - who was booked in the first half for handball to concede a penalty to allow Stjarnan back into the game - was penalised in injury-time for tugging back substitute Rolf Toft to concede another spot kick. The experienced midfielder had his heart in his mouth, thinking that Danish referee Michael Johansen was going to issue him with a second yellow card, which would have ruled him out of the second leg at their Samsung Vollurinn ground.
Lasley admitted: "At the time it was just initial disappointment at the way the penalty was conceded, but after it I probably looked back and I could have had a second yellow. I think I would have stuck my head straight in the oven if that was the case!
"It was one of those situations and I didn't have a great night's sleep after that. But it's gone now and we just need to look forward and I'm certainly determined to bounce back from it on a personal level and try to help the team any way I can to progress. I just got myself in awkward positions and I was disappointed, but they created a couple of good chances outwith that and I don't think 2-2 was an unfair reflection in the game.
"To be fair to their players they weren't looking for a second booking which I was glad about because that might have got the referee thinking. I think they were too busy celebrating the fact they had a penalty so late on.
"From being lucky to be here, I just hope to play a part in what's hopefully going to be a good night. But thinking back there's every possibility I could have been suspended for this and I would have been gutted."
Motherwell face a tricky second leg on Stjarnan's artificial surface tomorrow - a pitch which is not one of the newer versions which are popular in Scotland. But the 34-year-old will not be using that as a reason if Motherwell do not go though, to face either the Polish side Lech Poznan or Nomme Kalju from Estonia.
He said: "We're not looking to use the pitch as an excuse. We will just play the conditions as they are. If you ask most footballers they'd prefer to play on grass, but it's not to be and we've trained on Astroturf this week at the Braidhurst Performance School to prepare.
"I'm old enough to remember the really old Astroturf pitches and they've certainly come on since then because they used to be almost like a carpet. The newer the pitch the better but it's not something in our mind.
"We just want to go out and win a game of football regardless of the surface and we believe we're good enough to do it. We know we're in a game and we just need to make sure we're the better team on the night.
"We've picked ourselves up since last week but there's no doubt from their point of view it's a good result. A couple of away goals in Europe are always handy and scoring so late on, if the shoe was on the other foot, it would have given us a boost.
"But we feel we're more than capable of going and getting a result and we go into the game with confidence. The biggest disappointment for us is that we were in a comfortable position, two goals up, and we let them back into it.
"They might have that edge on us in terms of sharpness with them being into their season but by the end we won't be looking for excuses - we just want to come out on top."