The long-standing judge is unable to be part of the upcoming series due to restrictions preventing him from travelling to and from the US, where he judges Dancing With The Stars.
Speaking to The Sun, he said: “I am so sad and frustrated, but there is nothing anyone can do.
“Anton was the obvious choice to replace me.
“I was never asked my opinion, but I wasn’t surprised. He was desperate to get that judging role, so I’m sure he is delighted.”
Joking that Anton “needs the money”, Bruno also said that he will not be watching him on the panel as it “would not be fair”.
He said: “It’d be weird, like watching an ex with someone new — you just get on with it honey.
“It’ll do me no good as people will ask me what I think and I don’t want to stick my nose in when I’m not part of it. I think it’s very naff.”
Bruno also said he could still return to Strictly next year, should he be invited back.
“It’s totally up to them. If there’s no Covid and they want me, I’ll be back,” he said. “But they may say, ‘Anton was great, we don’t need you’.
“I’ll do something else. It’s like James Bond actors, I’ve done my stint. You cannot be desperate, if you start down that path you’ll go insane. I won’t be second best.”
Anton has made no secret of his hopes to join the judging panel in the past, having previously auditioned for the role of head judge prior to Shirley Ballas’ appointment.
Strictly Come Dancing returns to BBC One in the autumn.