The Italians drew 2-2 in Greece against Egaleo, a result which sends Middlesbrough, Villarreal and Partizan Belgrade through as the three qualifiers from Group E.
In-form AZ Alkmaar, Benfica and Sevilla also advanced to the knockout rounds, as did Lille who were not in action on Thursday.
The group phase is new to the UEFA Cup this season with eight groups of five teams with the top three going into the last 32 where they are joined by eight teams from the Champions League.
Lazio, 13th in Serie A after several key players were sold in the close season to offset financial problems, needed to beat Egaleo to have any chance of extending their European involvement into the New Year.
They fell behind after seven minutes when Ioannis Chloros netted from close range but Roberto Muzzi thumped home a free kick to quickly equalise.
Muzzi's second on 36 minutes after a through ball from Paolo Di Canio gave Domenico Casi's side hope but a fine finish from substitute Anastasios Agritis soon after the break made it 2-2.
Lazio's failure to win meant that Partizan's 1-1 draw at home to last season's semi-finalists Villarreal was good enough for both to progress.
Midfielder Rodriguez Cazorla beat the offside trap to fire the Spaniards ahead early in the first half before Ivan Tomic's penalty levelled it midway through the second half.
NINE WINS
Dutch high-flyers AZ Alkmaar continued their fine run as a 1-0 victory at home over Rangers put them clear at the top of Group F and into the next round.
Dutch international Danny Landzaat finished off a superb team move to net the only goal on eight minutes as Alkmaar made it nine successive wins in all competitions.
Rangers need a point from their final game at home to AJ Auxerre to go through.
Auxerre, who had failed to score in their previous two group games, hit two inside the first five minutes on their way to a 5-1 rout of Poland's Amica Wronki. Belgian Luigi Pieroni hit a hat-trick for the Ligue 1 side.
Sevilla booked their place in the last 32 when they came from a goal behind to claim a 3-2 victory over AEK Athens in Group H, Brazilian striker Julio Baptista scoring the winner from the penalty spot two minutes from time.
AEK, who lost both their previous matches, took the lead in the 10th minute when striker Nikos Liberopoulos guided home at the far post, but Sevilla equalised soon after when Baptista headed in from a corner.
The home side went ahead through Antonito before Stavros Giorgiopoulos scored with a thunderbolt to restore parity.
Baptista sealed victory for Sevilla to the delight of the 35,000-strong home crowd when he converted from the spot after substitute Kepa Blanco was brought down.
In the other group game, Germany's Alemannia Aachen scored in the last minute for a 2-2 draw at home to Zenit St Petersburg, a result which sends Lille through with a game to spare.
Slovenian Zlatko Zahovic netted twice as Benfica coasted through from Group G with a 3-0 away win over Beveren, who have now conceded 14 goals in three group games.
The Flemish side were not helped by the third-minute dismissal of goalkeeper Boubakar Barry. The final is in Lisbon on May 18.
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