The 21-year-old has returned to Palace on a season-long loan deal, 18 months after moving to Old Trafford from the Eagles.
Zaha, who was also loaned to Cardiff City last season, hopes that he can force his way into Van Gaal's plans with his performances during his latest spell at Selhurst Park.
"I signed for a couple of years at United so the goal is to do my best here for the season and go back and make sure I get back into the team and the England set-up," he told reporters.
"It is just great to be playing again. There is nothing like being out on the pitch and the crowd singing your name. It was a bit frustrating. What am I doing if I am not playing?
"I know how everything works here and the gaffer just wants to give me game-time and wants me to improve so I am just glad I am back."
Zaha featured in Palace's goalless draw with Burnley on Saturday.