Following defeat on the road against Leinster and Toulouse in Pool 6, Leicester Tigers were looking to win their remaining fixtures to claim a quarter-final slot in a competition which they have won twice.
But four penalties from Andy Goode were not enough at Murrayfield as Edinburgh clinched victory thanks to tries from Scotland internationals Ross Ford and Phil Godman, who also kicked seven points.
“Everybody in the dressing room is very disappointed, very sad,” said Tigers head coach Loffreda. “It hurts because we are capable of playing much better than that.
“It was a bad day for us and it was a good day for Edinburgh. We made a lot of errors, we lost the ball too many times and did not put enough pressure on them when we had the ball.
“I think Edinburgh played very well, they were good in defence and they looked after the ball.
“We had a poor day. It is frustrating because you always try to improve from one weekend to the next but in this case we went down from last weekend.”
Loffreda said Tigers knew Edinburgh would pose a bigger test than they did in the first meeting at Welford Road, when the hosts won 39-0.
“They have been working very hard since our first game and we knew that we were going to find a different team,” he said. “They played with a lot of heart and passion, and played an intelligent game.”
Tigers host Leinster, led by Ireland captain Brian O’Driscoll, in their final Pool 6 game next Saturday (kick-off 3.30pm).
“We have to pick ourselves up again for next week, but rugby is like that, you have to deal with those things,” said Loffreda.