Relieved boss Steven Gerrard admits Rangers should have left Hamilton empty-handed after putting in their worst display of the campaign.
The Ibrox side have been rampant this term on their march towards the club's first title win in a decade.
But there were well off the boil at the Foys Stadium as they allowed Accies to deservedly rescue a 1-1 draw with the last kick of the ball.
Brian Easton's own goal looked to have given Gers a lead they had done little to merit.
But Brian Rice's basement boys – who had been foiled umpteen times by Allan McGregor – finally found a way past the Ibrox stopper in the fifth minute of stoppage time as Ross Callachan handed his team a precious point.
The result will not alter the eventual destination of the title with Rangers still 21 points ahead at the top – but it could prove vital to Accies, who trim the deficit at the foot of the table to Ross County back to three.
"I am disappointed and I am frustrated at our own performance – I'm frustrated at myself," said Gerrard, who confirmed Rangers will appeal against Kemar Roofe's Notice of Complaint for last week's studs-up challenge on St Johnstone's Murray Davidson.
"When you take the lead but concede with the last kick of the game it's quite natural to feel like that.
"But I think when the dust settles I'll be quite relieved we've taken a point away today because I don't think we deserved anything out the game.
"It's the easy way out to say it's a bad day at the office. We had one of them at St Mirren and that's the reason we can't win a League Cup.
"Today was worse. I thought that was our worst performance of the season. Individual performances today weren't good enough.
"Our keeper has been the busiest of both goalies and kept us in the game. He's the reason we're taking a point out of the game.
"It would have been a smash and grab from us.
"So look we got what we deserved. We could have got a worse result but we never really looked like a Rangers team until we made some changes. I thought the subs did really well.
"The players up until this point have been absolutely terrific – but I can't find praise for that performance today."
Rice's side were hammered 8-0 when the teams last met at Ibrox back in November but the Hamilton boss said a victory would not have flattered his team this time.
"From my point of view, I think a point is the least that we deserved for our bravery," he said.
"It just shows you the spirit that we have got here and the belief that we have got that we didn't let the heads go down. To go to the 94th minute against Rangers and get that equaliser says a lot for the lads.
"You get that feeling sometimes that it won't be your day when you are at the sidelines but I had a belief in them.
"At half-time I told them if we lost a goal, we had to go again.
"I don't want us to ever give up and I don't want to see us feeling sorry for ourselves. I am shouting that, telling them to keep going and Ross Callachan, he missed a really good chance at 0-0, but he is in there. I said to him to keep getting in, keep getting in.
"It doesn't matter when it is, something will fall for you and it happened. But I am proud of the boys. I thought it was a really top-class performance.
"We are still bottom of the league. We have four away games coming up now and it is a tough schedule for us but the next game is the biggest game."
