Van Gaal has decided against signing a striker in the transfer window so far because he believes Rooney can score at least 20 goals for the club.
Despite letting Robin van Persie and Radamel Falcao leave over the summer, the United boss is determined to stick with Rooney, Javier Hernandez and James Wilson as his three main strikers.
And despite the recent criticism of his performances, the United captain is sure he will not let his manager down this year.
"I'm an honest guy. I know when I don't play well and against Aston Villa I was below my standards," Rooney said after United's 3-1 win over Club Brugge on Tuesday night.
"It's not a game which I want to look back on but obviously that happens in football. You'll have nights like that and you have to move on.
"It's early on in the season. We are just three games in. I've experienced this (criticism) before and the goals will come, I know that.
"I understand I have to be the one who's going to lead that line for us and try and find the goals for us."
Rooney spent part of last season in a deeper midfield role but returned to his favoured striker's position on United's pre-season tour, when he scored once in four matches.
Rooney insists he still knows how to operate as a lone striker, despite having not occupied that position on a regular basis for three years.
"My mind is clear. I know how to play the role," said Rooney, who will start up front for United against Newcastle on Saturday.
It's just a case of getting the chances and taking them, which I'm hopefully going to do soon.
"I've always enjoyed playing against Newcastle, so hopefully on Saturday I can open my scoring."
While Rooney failed to bag in his ninth successive match, Memphis Depay stole the show at Old Trafford on Tuesday, scoring two and setting up Marouane Fellaini for the third goal, which puts United within touching distance of the Champions League group stages.
Rooney feels the presence of the powerful Dutchman will help him break his duck.
"It's important that we all chip in," Rooney said.
"Memphis managed to get off the mark this season. I've had one bad game this season and everyone's all over it.
"I know, I've had that throughout my career but hopefully at the weekend I can get off the mark."
Despite his disappointment in front of goal, Rooney still enjoyed being part of United's first Champions League game in 16 months.
The United captain has missed playing in Europe's top club competition and does not want to see any slip-ups from the team in Wednesday's second leg in Belgium.
"The Champions League is what you want to play in," said Rooney, who was part of the United team that lifted the trophy in 2008.
"It's a great feeling stood there before the game when the music comes on and that's when you know how special a tournament it is.
Still, there's an important game for us next week to go and finish the job off but Tuesday was a good result for us in terms of starting well."