The England forward did not travel to Emirates Stadium for the game, which United lost 3-1.
Ten Hag said Sancho had not reached the “level” required to be included.
“Please don’t believe everything you read,” Sancho wrote on social media.
“I will not allow people saying things that is completely untrue, I have conducted myself very well in training this week.
“I believe there are other reasons for this matter that I won’t go into, I’ve been a scapegoat for a long time which isn’t fair!”
Sancho, 23, moved to Old Trafford from Borussia Dortmund for £73m in 2021.
However, he has struggled for consistent form and has scored nine league goals and provided just six assists in his 58 appearances.
Explaining his decision not to pick Sancho for his squad to travel to Arsenal, Ten Hag said: “Jadon, on his performances in training we did not select him.
“You have to reach a level every day at Manchester United and we can make choices in the front line. So for this game he was not selected.”
Sancho insisted he would continue to fight for his place at the club, adding: “All I want to do is play football with a smile on my face and contribute to my team.
“I respect all decisions that are made by the coaching staff, I play with fantastic players and grateful to do so, which I know every week is a challenge.
“I will continue to fight for this badge no matter what.”
In February, Ten Hag spoke of his pride in “magnificent” Sancho after the winger made a goalscoring return to the Premier League.
He had spent three months battling physical and mental issues, with Ten Hag at one point saying the England international was not fit enough to play.
Sancho returned to action in the EFL Cup semi-final win against Nottingham Forest on 1 February and a week later sparked a comeback against Leeds in the Premier League, scoring the equaliser in a 2-2 draw.
