Aberdeen manager Stephen Glass declared job done in Gothenburg but admitted their Europa Conference League tie was more frantic than necessary.
The Dons gained control after a difficult start but a facial knock for Jay Emmanuel-Thomas affected them early in the second period and BK Hacken went two up by the midway point of the half to reduce Aberdeen's aggregate lead to 5-3.
The Swedes soon had a man sent off though amid a flurry of yellow cards, including one for Glass and another for substitute Declan Gallagher – before he came off the bench – for kicking the ball away.
Aberdeen were comfortable thereafter and missed more chances before going through to face Icelandic side Breidablik despite a 2-0 defeat.
Glass said on his club's website: "The task before we kicked a ball at Pittodrie was to get through to the next round and we've done that.
"Tonight was maybe a little bit more frantic than it needed to be. First half we had a lot of chances, big opportunities to put the game to bed and we didn't take them. As a result, we ended up hanging on a little bit.
"It did get frantic second half, but we expected that. They're good players, good professionals and they had no choice but to throw everything at us then, which they did.
"We knew what it was going to be like and for the most part, the boys coped with that.
"We were up against a good team that could play with a more carefree attitude because of the first-leg result, where we were fantastic. It was almost a consequence of that scoreline that meant that it was that bit harder tonight.
"Saying that, we know we need to be better than we were, but we won't come up against a side that's going to be as free as that every week."
Emmanuel-Thomas is expected to be fit for Sunday's cinch Premiership opener against Dundee United.
"Jet got a decent sized cut above his eye but we think he should be fine for Sunday," Glass said.
"Their guy headed him and not the ball but the officials didn't see that. Other than that, everybody's come through unscathed."