Allen was aggrieved that the referee had failed to spot a "blatant" foul and suggested that cheating "seems to be a trait" amongst Chinese players.
However, the 26-year-old has now conceded that his comments may over overstepped the mark.
"Following my recent comments in the press conference after my first-round defeat to Cao Yupeng, I would like to formally apologise to anyone who may have been offended," admitted Allen, who will face disciplinary action for the comments.
"Having taken some time to reflect on my comments I can appreciate that I overstepped the line at a time when I was heavily influenced by the emotions of a disappointing defeat. I would like to take this opportunity to apologise to Cao Yupeng if he felt that my comments were insinuating he were a cheat.
"I stand by my opinion that the shot in question was a foul, but I also stand by my previous comments in the press conference that Cao was the better player and fully deserved to win. I genuinely wish him the best of luck for the rest of the tournament."
Yupeng awaits the winner of the match between Ryan Day and Ding Junhui.