The Clydesdale Bank Premier League leaders now face St Mirren in the Co-operative Insurance Cup final and Little believes the scare against United could serve as a timely reminder to those who felt silverware was inevitably heading for Ibrox.
"It felt like a loss at the end of the game but the fact we are still in the cup was the only positive we could take from it," Little said. "When we're in that position we're always fairly confident and tend to close out games well.
"Whether it was a bit of complacency or whatever it was, it's very disappointing we let it happen.
"I think it was the wake-up call that we needed and the manager let us know that. Hopefully in the league as well it will stop any complacency creeping in. There hasn't been any talk of the treble amongst the boys.
"You can't look two games ahead because there is a game coming every few days.
"Everyone is getting ahead of themselves so hopefully the fact that we have slipped up might calm people down a little bit."