A week after netting in the first round of UEFA Europa League qualifiers, Socceroos midfielder Mustafa Amini was unable to spur his team to victory in a 0-0 draw against Elfsborg in round two.
The Danish side now travels to Sweden needing at least a goal to progress to the next round.
Copenhagen is in a strong position heading into the second leg against Welsh side Newtown, but would perhaps have expected more than the 2-0 scoreline it produced at Parken Stadium.
Benjamin Verbic nodded home a second-minute opener, and Kasper Kusk gave the Danish side a two-goal cushion when he lashed home on the counter-attack in the 74th minute.
Rosenborg will head back to Norway with a 1-0 lead against Icelandic outfit KR, but it needed a 56th-minute penalty from Pal Andre Helland to pick up the win.
Zilina and Stromsgodset were 2-1 victors at Dacia and Mlada Boleslav respectively, while Brondby, Mladost and Wolfsberger won 1-0 on the road at Beroe, Kukesi and Shakhtyor, while Jelgava achieved the same result at home to Rabotnicki.
AIK defeated Shirak 2-0, Kairat went one better in a 3-0 triumph at home to Alashkert and Apollon put one foot in the next round with a 4-0 rout of Trakai.
The matches between Hapoel Be'er Sheva and Thun, and Cherno More and Dinamo Minsk both finished 1-1, Skonto was held 2-2 at home to Debrecen.
Zoran Nizic's 90th-minute goal handed Hajduk Split a lifeline as it went down 3-2 at Koper, but Beitar Jerusalem's hopes appear all but over after it suffered a 5-1 battering at Sporting Charleroi - the visitor finishing the match with nine men.
There were 1-0 home wins for Trabzonspor, Slovan Bratislava, Cukaricki and Legia Warsaw against Differdange, University College Dublin, Qabala and Botosani respectively, while Zeljeznicar and Astra won by the same scoreline away at Ferencvaros and Europa League debutant Inverness Caledonian Thistle.
Fellow Scottish side Aberdeen fared better in 3-0 win at Rijeka, while Odd won 2-0 at Irish outfit Shamrock Rovers. Vaduz earned a solid 3-1 win against Nomme Kalju, while Vojvodina is well placed having beating Spartaks 3-0.
Rounding off the action, Inter Baku won 2-1 at FH, while the matches between Slask Wroclaw and IFK Gothenburg, and Jagiellonia Bialystok and Omonia Nicosia ended in 0-0 draws.