United boss Van Gaal smashed the British transfer record to bring Di Maria from Real Madrid to Old Trafford, spending £59.7 million on the Argentina man.
Di Maria showed his class on Sunday, scoring and providing an assist in United's first win of the season - a 4-0 thrashing of QPR.
United spent more than £150m in the transfer window as Ander Herrera, Luke Shaw, Marcos Rojo, Daley Blind and Radamel Falcao also joined.
And Di Maria is hungry to prove his worth to the United fans and Van Gaal.
"Van Gaal was really important for me, in order to come here," Di Maria told Perform.
"[He] was one of the first person [people] who spoke about bringing me here. The coach always has the last word about the players he wants.
"I am really grateful to him because thanks [to] him I am now playing for United.
"I keep trying to improve every day and for that reason I wanted to come here to United. I needed to change my life. I will try my best to play the right way.
"I will try my best every match and show my arrival at Old Trafford was worthy."
United - who finished seventh last term - have made a stuttering start to life under Van Gaal.
They took just two points from their first three Premier League matches and were knocked out of the League Cup by third-tier MK Dons in a shock 4-0 defeat last month.
But Sunday's win on home soil was particularly encouraging as new signings Di Maria, Herrera, Blind and Falcao all looked the part.
And Di Maria is convinced the club can kick on and challenge for a top-four finish.
"Manchester United are trying to grow," he added.
"We already know we didn't start the Premier [League] in the right way. [But] those things always happen in football."
Di Maria and Manchester United will next be in action at Leicester City on Sunday.
