The Argentina striker is yet to agree an extension to his Juve contract, which is due to expire at the end of the season, despite long-running negotiations.
Recent Italian media reports suggested he was unhappy with the club's stance in talks, and the 28-year-old appeared to send a message to the Juve hierarchy when he reacted to firing home the opening goal in the 19th minute by staring at club directors in the stands.
However, Dybala downplayed the gesture after the game.
"I invited a friend and couldn't find him, there were a lot of people," he told Sky Italia.
Asked if that explanation should be believed, Dybala replied: "I don't know, that is up to you."
"I have nothing to prove to anyone. The club decided that we will talk in February or March, I am available to the coach," Dybala then told DAZN.
Juve remain fifth but moved on to 41 points, level with Atalanta in fourth, who have two games in hand. Udinese are 14th with 20 points.
Allegri marked his 300th game as Juventus coach, becoming the third manager to reach the landmark after Giovanni Trapattoni and Marcello Lippi.
His task was made easier by the fact that the visitors were suffering from a COVID-19 outbreak that left nine players and three staff members unavailable.
Only 5,000 fans were allowed into the Allianz Stadium as part of new restrictions to fight the spread of the virus, but those who turned up were eager to see their side respond to an Italian Super Cup defeat by rivals Inter Milan on Wednesday.
Dybala sent them on the road to victory when he curled in a finish, but the striker's reaction is sure to spark further speculation about his future.
Udinese enjoyed good spells either side of the break but struggled to carve out chances, and McKennie eventually put the result beyond doubt by heading home a Mattia De Sciglio cross on the 79th minute.