Toney took the video while on holiday in Dubai, where he relaxing with the Premier League on a two-week break.
Toney maintains the video has been edited but has nonetheless accepted he was in the wrong.
In a statement on Twitter, Toney said: "I am aware of a video of me that was published on social media today, taken in Dubai where I have been on holiday during the winter break. In it, I used language that was unacceptable.
"The video was cut short and edited, but I have to accept the impact this has had and I realise I should not have put myself in this position.
"I have explained to the gaffer what happened and apologised to him but I also want to apologise to all Brentford fans. I respect the way you all support the team and I have to say how much I love playing for the club and for you.
"I'll be back at training next week, working hard to score more goals to win us more games for the rest of the season."
Toney is Brentford’s top scorer in the Premier League this season with six goals in 21 games.
