Rangers manager Ally McCoist rued his side's poor defending but Peter Houston was thrilled as Dundee United beat the SPL giants 2-0 in the Scottish Cup.
Rangers were poor throughout the game and lost to first-half goals from Gavin Gunning, with a bullet header and Johnny Russell's delightful finish.
McCoist showed humility in defeat but the latest loss piles more pressure on the Rangers chief, who lost top scorer Nikica Jelavic to Everton last month.
"You've got to give United a lot of praise especially for their first half performance, they took their chances," he told Sky Sports.
"I thought our defending was very shabby to say the least for both goals. I thought we could have defended the cross better [for the first goal].
"For the second goal I think we were posted missing a little bit. I don't really think we put enough pressure on the United goal today.
"I know their keeper made a few saves in the first-half but at the same time I was disappointed in that aspect."
Houston, though, felt his side were deserved winners as they caused a major upset by knocking Rangers out of Scottish Cup at Ibrox.
"It's a great feeling coming to Ibrox at any time and winning because Rangers have got a good squad of players," he said.
"But today in the first half I felt we were the better side, and we got the goals but we still had Dusan Pernis to thank for two good saves."