Wenger accused Shawcross and Robert Huth of fouling Tottenham goalkeeper Heurelho Gomes as Stoke rallied to find an equaliser in a Premier League game at the Britannia Stadium last month.
Shawcross has been the subject of criticism from Wenger on a number of occasions, following Stoke's home win over the Gunners in their first Premier League campaign and also last season when a clumsy tackle by Shawcross resulted in Aaron Ramsey sustaining a broken leg.
"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," Shawcross told the Stoke Sentinel. "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.
"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 reacted angrily when Wenger's comments were first published on Arsenal's official website - making complaints to the Football Association, the Premier League and to Arsenal. The Gunners removed the comments from their website but no further action was taken by the governing bodies.
Wenger had said: "It is more rugby on the goalkeepers than football. When you see the way Shawcross kicked Gomes, how Huth pushed Gomes in the goal, you cannot say that is football anymore."