The Gunners ended a run of four straight defeats in all competitions on Thursday with a 2-0 victory away at AC Milan on Thursday night, putting Arsenal Wengers side on course for the quarter-finals in the only competition they can still win.
A 2-1 defeat at Brighton last weekend leaves Arsenal 13 points adrift of the Premier League top four, although Wilshere hopes to see his side use their midweek win at the San Siro as a platform for the rest of the season.
"If anyone tells you you havent got to prove anything to anyone, they are wrong," he said. "You are always trying to prove yourself to people and play well in the next game.
"We know we havent been good enough. We are aware of it. We have got to use this win as a target. We have got to reach these levels every week."
Watford sit ninth in the table following back-to-back home victories, with the Hornets looking to complete the double over Arsenal after winning the reverse fixture 2-1 at Vicarage Road in October.
Meanwhile, Arsenal will be out to avoid an unwanted record under Wenger, having previously lost four league games in a row back in March 1995 under caretaker Stewart Houston.
Arsenal will be sweating on the fitness of a number of players ahead of Sundays Premier League clash against Watford, with Hector Bellerin (knee) unlikely to recover in time after missing Thursdays win at the San Siro.
Nacho Monreal (back) is also expected to be absent and Alexandre Lacazette (knee) is missing, while both Sead Kolasinac and Calum Chambers came off injured in Italy. Pierre-Emerick Aubameyang is available for selection having been ineligible in Europe.
Watford will still be without midfielder Tom Cleverley (thigh), who has returned to training after being sidelined since January.
