Wenger accused the 22-year-old centre-half and team-mate Huth of continuously fouling Tottenham goalkeeper Heurelho Gomes during last month's Premier League clash, saying they were acting more like rugby players than footballers.
Stoke have complained to the league about Wenger's comments, as it is not the first time the Arsenal boss has aimed criticism at Shawcross.
Earlier in the year Gunners midfielder Aaron Ramsey received a horror leg break at The Britannia after going in for a tackle with Shawcross, and Wenger was furious with the challenge in the aftermath of the game.
However, Shawcross is certain he did not foul Gomes against Spurs and believes the French coach is pursuing a personal vendetta.
He told The Sentinel: "I don't mind people having their opinions, but if it's not a game involving his players then I don't see the point of bringing up me and Huthy.
"I've watched the video again and at no point did I go anywhere near Gomes.
"I didn't think I had, but I didn't want to say I hadn't touched him before looking at the whole video to make sure."
Shawcross added: "He's obviously got something against me. It's just weird. He brings my name into it.
"He always seems to have a problem with Stoke, our manager and certain players.
"Criticism doesn't bother me, unless it's a false accusation like this one.
"It's just disappointing he came out and said something that wasn't needed.
"He could have said there was a problem week-in, week-out in the Premier League, but he shouldn't have named individuals."
Stoke have yet to pick up a point in the league this season and Tony Pulis' men will look to rectify that when they take on Aston Villa next Monday.