The 22-year-old winger struggled for playing time during Van Gaal's two-year reign at Old Trafford and recently claimed that his progress stopped under the Dutchman.
Belgium international Januazaj made a move to Sociedad earlier this summer, joining permanently for a fee believed to be around £9m, and he is determined to prove a point to his growing list of critics.
"If I score a goal I will dedicate it to Van Gaal," he told AS. "I don't want to talk about him but everyone knows how many problems I had with him. We didn't have the best of rapports.
"It wasn't easy, it's very frustrating and difficult when you are in a situation like that. I didn't have many possibilities to play. I spent a long time on the bench and that makes you lose confidence and minor injuries emerge.
"Many times I wouldn't play as a starter and you struggle to shine without continuity. The coach would put me in positions that I didn't know how to play in and I had little experience in. I hope that one day, I can shut up all those people that criticised me."
Januzaj made 38 appearances under David Moyes in all competitions, but started just seven times in the Premier League in Van Gaal's first campaign before being farmed out on loan to Borussia Dortmund.