Wolves are condemned to finish bottom of the Barclays Premier League table and signed off at Molineux on Sunday with a drab goalless draw against Everton.
It at least brought to an end a run of nine successive home defeats but was only the fourth point the club have picked up in 12 games since Terry Connor took over from Mick McCarthy as manager in February.
The fans mixed black humour with anger directed towards the board at the end of a miserable season, and Edwards wanted to assure them the players understand their frustrations.
He said: "They feel just the same as us - we're ashamed, we're upset and we're disappointed at the way we've played because the manager has put faith in the players he selects and we haven't been good enough this season.
"And we feel we've let the club down as a whole, from the people at the top to TC (Connor) especially, because everyone loves him."
Connor will find out after the final game of the season at Wigan next Sunday whether he will be given the chance to lead Wolves in the Championship.
Despite the poor results, the players have been unanimous in their support for McCarthy's former assistant, and he has no doubt they have given everything to the cause.
"It's very nice that they should say that," said Connor. "I can't ask for any more in terms of their endeavour, their honesty and their approach to the games and training, and to everything I've tried to do."
Sunday's game could not have been a greater contrast to Wolves' 4-4 draw with Swansea a week before, with neither goalkeeper unduly tested.
Everton certainly had the better of the game and had the ball in the net twice only for Nikica Jelavic and Denis Stracqualursi both to be denied by offside flags, erroneously in the former's case.
Edwards admitted it was not one of Wolves' better performances, but he was relieved that for once they managed to get something out of the game.
"If we don't play well, we need to make sure we don't lose and we managed that, it's just unfortunate that we haven't done that all season," he said.
"We didn't play well but I think that was because the lads were all mentally jaded after the last few weeks.
"We prepare right every week and we did for this game too but, for whatever reason, I thought the boys looked very sluggish in the first half and we were lucky to come in with the score still 0-0.
"But at least it was 0-0. In the past, when we haven't played well, we've been 2-0 down.
"We showed a bit of a fight at the start of the second half and created a few chances, but in the end we were happy with a 0-0 draw because we didn't play as well as we would have liked."
It was a frustrating afternoon for Everton, who must now beat Champions League-chasing Newcastle next weekend to be sure of clinching seventh place ahead of Liverpool.
Manager David Moyes has been reluctant to cite topping their derby rivals as a motivation, but his assistant Steve Round conceded it would be a sweet moment.
He said: "This was an opportunity but we were away from home at a team desperate to send their fans home happy and come away with a win, so it was always going to be a tough game.
"Next week's at Goodison, we're formidable at Goodison and no team would want to come there on the last day of the season having to win. We go in there confident, we're playing well and we know that if we win that game we'll finish seventh.
"The players want to finish as high up the league as they can, and if we can finish above Liverpool then even better."