Hugo Rodallega scored for the Latics with a lovely free-kick to bring hope following Rangers goals from Heidar Helguson and Akos Buzsaky. Tommy Smith sealed all three points with his late strike.
Speaking about the game, Latics boss Roberto Martinez said: "Today it was a clear sign we couldn't cope with the two injuries we had Alcaraz and Crusat.
"It is quite clear we need to help the players with a couple of fresh players. It is more important than the positions the characters we get and they come in and give us a real help.
"Every point is going to be huge and every small margin is going to be important.
"We were disappointing individually. We need to understand in the next 16 games in a typical relegation scrap you need to fight and find that understanding needed to affect a game.
"I think we will learn a lot today and we need to be better individually for these sort of scraps."
The Latics are expected to have to rely on loan signings during the January transfer window as all the transfer money has now been spent.