Deeney made the remarks after Arsenal's 2-1 defeat at Vicarage Road last weekend, when his introduction as a substitute unsettled the Arsenal defence and turned the game in Watford's favour.
But Wenger, speaking ahead of the Gunners' visit to Everton on Sunday, effectively pointed to his players' medals as proof of their quality and character.
âThe only response we have to give is on the pitch and not listen too much to what people say,â he said.
âIf you look at these players and what they have achieved in their careers, I think that speaks much more than any sentence at a post-match press conference.
"When youâre questioned, in our job there is only one response and that is on the pitch."
The Frenchman was just as dismissive of reports that Germany midfield player Mezut Ozil wants to join Manchester United in January.
âWe have to deal with all kinds of speculation when the players are at the end of their contracts,â he said.
âOn the other hand, to be professional is to give 100 per cent as long as you are somewhere. For the rest, we came out many times and said thatâs the situation.
"The media can come out tomorrow and say that he extends his contract here. It will be exactly the same, it will not change anything. When you play the next game, commit 100 per cent.
Neither issue, he insisted, would affect his plans for the visit to Goodison Park, when Arsenal can pile extra pressure on under-fire Everton manager Ronald Koeman.
âI believe that at the moment I just focus on what is the best possible team for the next game and have no pre-conceived ideas if the guy will be 100 per cent committed or not, Wenger said.
Alexis Sanchez and Aaron Ramsey are expected to return to the Arsenal starting eleven, and Laurent Koscielny is fit to play after cramp forced him off towards the end of the Watford match.
Koeman, meanwhile, has complete faith that the players he signed in the transfer window will get his side's season back on track.
The Dutchman made a sizeable outlay to bring in Jordan Pickford, Michael Keane, Wayne Rooney, Gylfi Sigurdsson, Davy Klaassen and Sandro Ramirez but Everton find themselves languishing in 16th place in the Premier League.
âI still believe in the players, and I still believe in the signings that we made in the summer,â Koeman said.
âMaybe some people can have doubts about some of them at the moment but the future will tell everybody that the signings we made were really good ones.
âWe need to take the situation for what it is now and prepare our team for Sunday.
âOf course, we have discussions internally about the tough start, the fixtures, Europa League football but the position in the table is not where we need to stay and that is what we need to change.â
Koeman will decide whether to recall Phil Jagielka, Leighton Baines and Rooney against the Gunners after he rested the trio for Evertons 2-1 defeat to Lyon in the Europa League on Thursday.
James McCarthy is available again having recovered from the knee and hamstring problems which have prevented him from making a first-team appearance this season, while fellow midfielder Morgan Schneiderlin has shaken off a knock picked up against Lyon.