The 34-year-old netted twice for West Brom at Upton Park - his first and second goals for the club since his arrival in the summer - but has received criticism for his actions after pulling his side level in the 40th minute.
When asked for a comment on the accusations, Downing replied: "I’m aware of it.
"But it’s nothing to do with what’s been said. He’s dedicated it to a French comedian who he knows very well. It was a gesture he uses in his act. The speculation can stop now. It’s absolute rubbish. He’s totally unaware of what the problems were."
Since Steve Clarke’s sacking on Dec. 14, West Brom has secured three draws under the guidance of Downing.
Former Real Betis coach Pepe Mel was interviewed for the vacant managerial position but talks broke down between the two parties on Friday evening.
"All I’ve been told is to carry on," Downing said. "If anything comes before that I’ll gladly step down and support the guy who comes in. I’ve had no real contact with the chairman. I know you guys had picked up on the Spanish chap [Pepe Mel] but he had the interview and was not for the club.
"It’s unwise for me to get involved with all that. Because I then get distracted and I don’t want that to transfer to the players. [I want] the players to know I’m fully focused on what I want to do."