Shawcross was criticised by Wenger last week.
The Potters captain told The Sentinel: "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."