City had chances to go further ahead but an extra-time winner from Telma Encarnação – after she had levelled the tie – put the Portuguese side ahead before Carla Armengol added a killer third to rub salt in the wound.
Sporting Lisbon looked to get off to a quick start and assert their authority in the tie from the opening stages.
Lee Gibson was forced into action to deny Florencia Bonsegundo as she tipped an effort over the bar.
City had to work hard to keep their discipline and their shape with their most likely route to success coming through set-pieces.
It was through a free-kick just four minutes from the break when they got their reward for sticking to the game plan.
Lisa Evans floated a free-kick into the box with the ball flicked on for Koslova to head into the net at the back post.
As the game started to open up, City might have had a second when Linda Motlhalo had two decent chances to double their lead and give them a more comfortable cushion.
Her first was a long-range effort before she then snatched at an effort without getting any real power behind it.
City were left to curse their profligacy when Lisbon levelled minutes later.
A long ball split the City defence with Telma ghosting in to convert a left-foot effort and angle it beyond the reach of Gibson.
With no VAR in the Europa Cup, City felt as though they should have played the latter stages of the game with a numerical advantage after Koslova looked to have been taken out. However, play was allowed to go on much to the frustration of City.
It might have got worse for the Petershill side as Lisbon put them under immense pressure.
Telma whacked a free-kick off the post with just three minutes of regulation time remaining.
It set up a fraught finale as Lisbon kept them penned inside their own half as they toiled to get out.
Lisbon kept up the pressure and for the first time in the tie went ahead on the 100-minute mark.
The ball came in from the right-hand side and City were caught sleeping as Thelma was able to steal in between the two centre-halves with the striker’s header from close range leaving Gibson completely exposed.
With Lisbon firmly in control, Armengol added a third when she lifted the ball past Gibson.