Supporters vented their fury towards Morgan during a pitch invasion after the 2-1 defeat by Burnley on Saturday and further protests outside the ground.
But Moxey is adamant the board are committed to getting Wolves back on track even if the club suffer a second successive relegation.
Moxey said: "It goes without saying that Saturday's loss to Burnley felt like a devastating blow for everyone who loves Wolves.
"We have no illusions about the immediate future as the odds of remaining in the Championship are slim.
"However, with one game remaining the players have a duty to the club and its supporters to play one last match against Brighton, secure a win and hope against all hopes that other results go our way.
"As we've said previously, this season has been disastrous and everyone here is apologetic and regretful about the position the club is now in - facing relegation into League One with one match remaining is not acceptable for any Wolves side, let alone one that was in the Premier League a year ago.
"We understand supporters' anger and frustrations and at the end of the season we will attempt address the problems that have caused our downward spiral.
"The chairman remains committed to help put these issues right. He wants a brighter future for Wolves and the supporters."
The frustrations of around 300 or so angry Wolves fans boiled over as they invaded the Molineux pitch after Saturday's 2-1 home defeat to Burnley - actions being investigated by West Midlands Police and the club.
Amid the ugly scenes central defender Roger Johnson appeared to be jostled and stewards attacked while the home dugout was smashed, advertisement hoardings were ripped down and attempts were even made to bring down a goalpost.
Moxey today added: "As West Midlands Police have said, it was a disappointing end to what had been a trouble-free fixture. Wolves fans have given the players and the club tremendous support and have behaved exceptionally well all season.
"However, as we saw on Saturday, it only takes the actions of a small minority of fans to change public perceptions, which is unfair on the majority of supporters.
"A small number of fans, as passionate as they are about their club, were unable to contain their feelings and, at the end of the game, ran onto the pitch. Nevertheless, the actions of some these people were unacceptable and it's our duty to work with West Midlands Police to identify those who stepped over the mark."