The Gunners' hopes of lifting the FA Cup for a third consecutive year were dashed on Sunday as they were beaten 2-1 by Watford at the Emirates Stadium.
Goals from Odion Ighalo and Adlene Guedioura were enough to see Quique Sanchez Flores' side progress to the semi-finals, with Arsenal only about to reply two minutes from time through Danny Welbeck.
The north Londoners remain eight points off top spot in the Premier League and face an uphill task when they head to the Camp Nou to take on La Liga leaders Barcelona in the Champions League last-16 in midweek.
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Despite increased hostility surrounding his job, Wenger was in defiant mood following the latest defeat, telling reporters: “The next game is always a big challenge and you are always in the middle of a drama. It is becoming a farce. We have lost a game.
"We are sad and we want to focus on the next game. Arsenal have lost games before in history and we will lose again in the future. We will stick together and cope with it and prepare for the next one with complete belief.
"We want to make the impossible possible [in Barcelona] and we know we play against a very strong, strong side and it’s important we go there and focus and show a very good response.
"Supporters stand behind the club and we want to fight until the end of the season for every single game. That is what we did. What is going on at the moment is very, very difficult to take for the players but judge us at the end of the season.
"We have come to the end of a very, very long run in the FA Cup, so it is very sad, but we want now to focus on the next game.”