"When it comes to a semi-final or final you have to play very well to win and we didn't do that today," he said.
"In attack we just didn't have the control or the patience to hold onto the ball, to go through that extra phase in the first half.
"In the second half we showed what we can do and came right back into the game but it's a pity we couldn't sustain that."
Fly-half Finn Russell was taken to hospital after suffering a "facial and head injury" in the opening minute.
"It's a nasty looking injury," Gregor told BBC Scotland. "We hope it's not too bad."
Winger Sean Lamont said it was "a season's work gone down the drain."
"Credit to the boys, they dug in to the end, but I just think we were on the wrong side of the penalty count and weren't quite clinical enough," said the 35-year-old.
"For the boys that are leaving us it would have been nice to finish on a high but unfortunately we were just a little bit short.
"To lose a couple of guys [Russell and Fagerson] so early it does shift things but I think the guys that came on did a great job. These things happen, it's rugby unfortunately, it's the nature of the sport."