Two goals in each half on Thursday evening has more or less sealed the tie for the home side but despite the scoreline Stephen Baxter's men gave a good account of themselves against a top outfit.
Jordan Owens had an early chance for the visitors before IF Bromma forged ahead on nine minutes.
The Crues gave as good as they got during the opening 20 minutes and O'Carroll almost snatched an equaliser.
However, a superb run by Albornoz on 27 minutes saw him get behind the defence and fire past O'Neill to make it 2-0.
Bromma then had an effort cleared off the line by McClean and then O'Neill produced a fine save to prevent the home team from adding to their tally.
Just before the break Paul Heatley tried his luck from distance but his effort curled wide of the goal.
It was Heatley again with the chance to pull a goal back early after the restart but the keeper made a fine save.
Larsson then made it 3-0 on 62 minutes and not long after it was 4-0 after Heatley conceded a penalty and Barkroth scored from the spot kick.
Despite those blows the Crues kept pressing in a bid to grab a goal and they went close with efforts from Owens and Caddell.
The second leg of the second qualifying round tie will be played in at Seaview next Thursday, but the Swedes already have one foot in the next round.
Crusaders: O'Neill, Burns, Coates, Morrow, O'Carroll, Robinson, Caddell, McClean, Owens, Clarke, Heatley.
Subs: Leeman, Adamson, Snoddy, Cockcroft, Whyle, Dempster and McCrea.