Wilshere agreed that the players need to look at themselves after a disappointing performance against Watford, but deemed the Hornets striker's comments harsh.
Both Jack Wilshere and Wenger dismissed Deeney's remarks, with the former insisting it was unfair to question Arsenal's character.
The 25-year-old is quoted by The Telegraph as saying: "As a player, if your attitude is questioned, it's disgusting".
"For my players we must look inside and not outside and respect ourselves, as well". After that, the comments, that's part of the modern game.
The ex-England defender said: "He actually said to me off-air, he mentioned one or two players that we wouldn't make public, that he saw didn't look like they [wanted it]".
"People try to put us down, they always have".
'Having a bit of cojones, I think the word is. You can't question our character. Whenever I play against Arsenal - and this is just a personal thing - I go up and think "let me whack the first one, then we will see who wants it"'. We will move on. We will see in the next match and we will see what happens. "My opinion will stay between me and him". We have to deal with that.
Newcastle have made a good start to life back in the Premier League and sit ninth in the table after eight games.