Henderson was the hero for Forest as he saved two penalties in a 4-3 shoot-out success against Wolves after the quarter-final tie had finished 1-1 in normal time during which he made a number of other saves.
The on-loan goalkeeper, who kept out Ruben Neves and Joe Hodge spot-kicks, will be ineligible for the two-legged last-four tie against his parent club, unless United give written permission for him to play.
That appears unlikely after this display as Forest made it through to the semi-final of a competition where they hold special memories, having won it four times.
"I have only just thought of that, it is frustrating," Cooper said of Henderson's ineligibility.
"After seeing the night he had tonight, he was excellent in the penalty shoot-out but he was good in the game, more than good in the game.
"It's unfortunate. He's part of our group, he is so invested in the group and how we work, what we're trying to accelerate in terms of what we want to become.
"To do that you need a really good goalkeeper. Not only is he committing as a goalkeeper, he is buying into being in the city and the greater good of the club.
"It has put a dampener on it for me tonight."
There were ugly scenes at the end with a mass brawl between the two sides as bad blood boiled over.
Former Wolves forward Morgan Gibbs-White, who celebrated in front of the away end when his side won, was at the forefront of it, clashing with a number of his former team-mates.
Stewards had to intervene and both clubs are sure to be in hot water with the Football Association.
Cooper did not want to comment on the incident.
"I am not going to deny there wasn't one because there was but why it happened and how it happened and what happened, if I speak about it I wouldn't be completely clear because I don't know," he said.
"So I shouldn't really say anything."
Gibbs-White helped set up another Wolves old boy to put Forest ahead as Willy Boly prodded home from close range from a corner but Raul Jimenez levelled after the break.
Wolves thought they should have had a penalty after Matheus Nunes went down under a challenge, but referee Graham Scott waved away protests.
Wolves boss Julen Lopetegui said: "I'm disappointed we lost and didn't go to the semi-final.
"We had more chances than Nottingham but it is about the goals. We had chances in the first half and didn't take them.
"We scored one goal and had another situation. Nunes went to control, we have seen the image.
"Maybe I have to learn about the rules. It was very clear to me but the referee is the only one with the power to say yes or no.
"For me it was very clear, it is impossible to see on the TV and say it wasn't but there was no TV."