The Light Blues found themselves trailing after just 16 seconds at Tannadice, as United went on to secure a comfortable 3-0 win.
The result left Rangers with only the Irn-Bru Third Division title race to focus on this season, with Little admitting the players let the club down last week.
He said: "I don't think we expected it.
"It couldn't have been a worse possible start and, by the end, to be honest, it was embarrassing and humiliating.
"Everyone was disappointed to a man and we let ourselves down and we let the club down.
"It showed we're not quite as good as people maybe thought we were and I think we've got a lot to improve on.
"We have to now put on performances and entertain the crowd as much as we can.
"The only thing we can do now is make an impression on the league and try to impress and try to give the fans something to celebrate."
League leaders Rangers play host to nearest rivals Queen's Park tomorrow, aiming to extend the gap at the summit to 22 points.
Little said: "When you have a really poor result like we had last weekend, what you want most is another game to try to react and put things right.
"It's a great chance for us against Queen's Park to put right those wrongs and really try to put this league to bed."
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