The club's 35-year-old English back-up keeper was called into action for only the second time since signing last summer after Cammy Bell suffered concussion.
However, his first game at the Gers' ground - designated as a neutral venue last year because Hampden is out of commission - was to prove a nightmare as, with the League One champions trailing by 2-1 late in the game and looking for the leveller, he was dispossessed by Nadir Ciftci after taking a Richard Foster pass-back to allow the United striker an easy third.
"I didn't speak to anyone individually. I spoke to all the boys," McCoist said. "Every one of them is disappointed.
"It would be unfair and wrong of the me to single anyone out for errors.
"We missed chances and we gifted one or two goals.
"You win and lose as a team, although of course they were individual errors."
After a positive start from McCoist's side - who had been heavily criticised for losing the Ramsdens Cup final to Raith Rovers at Easter Road last week, with fans calling for his head - goals from midfielder Stuart Armstrong and wide-man Gary Mackay-Steven put the Taysiders two ahead before Light Blues defender Steven Smith pulled one back before the interval with a free-kick.
Rangers could not subsequently fashion anything like the two chances missed by Dean Shiels and Jon Daly in the first half and, when Simonsen's hesitancy allowed Ciftci to pounce, it was all over, leaving the former Rangers striker "bitterly disappointed".
"I thought we were the better team for the majority of the game but poor decisions cost us," he said.
"I thought we slit our own throat with the goals we lost and our level of finishing wasn't what it should be.
"We couldn't have asked for better chances. We even had a chance in the first two minutes with Bilel (Mohsni), so if you don't take your chances, you run the risk, especially with the way we defended for the goals, the last two in particular."
Much has been made of the standard at the League One champions as the Ibrox club play their way back towards the top flight after descending into administration and liquidation.
However, McCoist insists there has been a marked improvement since they were knocked out of the Scottish Cup by the Taysiders last season.
"it has just confirmed what we have always thought," he said.
"I thought we had a side of top-flight ability and that was possibly shown to be the case today, but it just confirmed that we have a long, long way to go.
"The last two defeats confirmed what we need to do and add to the squad.
"I think we are better than we were 14 months ago, but we need to be better again next year. We need to keep improving."
Dundee United boss Jackie McNamara admitted that Ciftci's goal eased the nerves as he braced himself for the possibility of a Rangers equaliser.
"It settled me down at that point," he said. "The second half was a bit frustrating with our decision-making and passing.
"We invited Rangers on to us, we were too deep, and I was just delighted to see it through.
"You are always cautious - they do carry a threat..
"I always felt the next goal in the second half was crucial and I was delighted we got it."
The former Partick boss paid tribute to the 11,000 or so United fans who added to the colour and noise inside Ibrox and who will make their way to Glasgow next month for the second time in four years to play either St Johnstone or Aberdeen, who go head to head in the other semi-final at Ibrox on Sunday.
"I am delighted and, for everyone connected to the club, it is such a great feeling," he said.
"The fans were fantastic from start to finish. It was a great sight to see all the tangerine - not just behind the goal but at the sides as well, as well as the vocal support they gave us.
"It was good to send them up the road happy. That's what it is all about."