Nigeria internationals Joe Aribo and Leon Balogun played all minutes for Rangers, however, they could do little to prevent the Gers from bowing out of the Champions League.
The Scottish Premiership side lost 2-1 at home to 10-man Malmoe FF at Ibrox Stadium on Tuesday night.
Steven Gerrard's men had suffered a 2-1 loss in the first leg and heading into the second leg, they needed at least a 1-0 win to sail through.
Rangers began the game on an impressive note by dominating ball possession and that paid off in the 19th minute when they took the lead.
Profiting from a quick free-kick, Ryan Kent found the opportunity to beat his marker before sending a cross to Alfredo Morelos who headed past goalkeeper Johan Dahlin.
Seconds before the half-time break, Malmoe had Bonke Innocent sent off for a second caution. The Nigerian was given his marching orders by referee Slavko Vincic for a high challenge on Connor Goldson.
Notwithstanding the numerical disadvantage, the Allsvenskan outfit came out determined in the second half.
Antonio-Mirko Colak levelled matters for them in the 53rd minute and four minutes later, he completed his brace after converting a pass from Niklas Moisander.
Thus, Rangers crumbled following a 4-2 aggregate defeat.
At the Huvepharma Arena, Youssef El-Arabi found the net as Olympiacos played out a 2-2 with Ludogorets Razgrad.
The Greek side were trailing 2-1 but the Morocco international restored parity from the penalty spot following a foul in the hosts' penalty area.
Four minutes to full time, Olympiacos had their Senegalese import Ousseynou Ba sent off for a second caution.
Despite playing with 10 men, Pedro Martins' men held their nerves to end the game 2-2.
With aggregate scores tied at 3-3, the teams were separated by kicks from the penalty spot and Ludogorets advanced after a 4-1 win.
Elsewhere, Sofiane Diop was among the goal scorers as AS Monaco strolled past Sparta Prague 3-1.
Heading into the game, the Ligue 1 side had nothing to worry about having won the first leg 2-0 in Prague.
However, they completed a double with an impressive win at the Stade Louis II, Monaco.
After a goalless first half, Gelson Martins put his team ahead in the 50th minute before Aleksandr Golovin doubled the advantage six minutes later after he was set up by Wissam Ben Yedder.
Although the visitors pulled one back through David Karlsson in the 78th minute, substitute Diop restored Monaco's two-goal advantage with nine minutes left on the clock.
Lastly, Cameroon international Nicolas Ngamaleu found the net in the first half as Young Boys silenced CFR Cluj 3-1 at the Wankdorf Stadium, Bern.
The result took them to the next round after a 4-2 aggregate win.