The loss has left Wolves three points from safety with just one match away at Brighton & Hove Albion left to play. Even a win against the Seagulls may not be enough to keep Dean Saunders's side in the Championship.
With relegation a real possibility, Moxey has taken the chance to apologise to the supporters for the team's performances this season.
"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," he told the club's official website. "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."
Following the final whistle at the weekend, a large number of Wolves supporters took to the pitch to voice their displeasure towards chairman Simon Morgan and Moxey and damage was caused to advertising boards and the dugouts in the process.
Commenting on those incidents, Moxey 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."
Wolves were relegated from the Premier League last year.