The BBC ballroom judge compared the professional dancer to the US president after Anton filled in for regular panellist Motsi Mabuse last weekend.
Motsi has been forced to miss two weeks of Strictly as she is currently self-isolating after an “urgent” trip to Germany.
However, Craig thinks Anton might have a hard time giving his seat back to Motsi, much like how Trump is yet to concede defeat in the US election.
Speaking on Thursday’s Lorraine, Craig said of Anton’s judging stint: “It was like a three-year-old coming in, sitting in his podium. He was loving himself sick, it was fantastic to see him sitting on the podium.
“I was absolutely delighted darling that finally he got the chance. Now I think he is going to be a little bit like Trump – difficult to remove.”
It was the first time Anton – who has been a professional on Strictly since its inception in 2004 – had sat on the panel, having previously made no secret of his desire to do so over the years.
Upon his debut on the panel on Saturday, Anton – who had already been eliminated from this year’s competition with partner, former home secretary Jacqui Smith – was met with a thumbs up from fans of the ballroom competition.
Meanwhile, Craig has also named Bill Bailey as the one to watch in this year’s competition.
“I am secretly actually loving Bill Bailey,” he told Lorraine. “I adore him. He just shocks me.
“Every time I see him dance, I am surprised, amazed and delighted. I never thought for one moment he would be able to do it. He doesn’t look like the type or the type of character… I love him, I would love to see him in the final.”
“I think he is brilliant, the dark horse of the competition,” he added.
Lorraine airs weekdays at 9am on ITV, while Strictly Come Dancing continues at 7.15pm on BBC One.