Falcao has endured a difficult start to his life at Manchester United, scoring just one goal in five appearances since his dramatic deadline-day loan move from Monaco.
The striker has struggled for fitness and is yet to complete a full game for the Red Devils.
The Colombian has been unavailable for the last month because of a calf injury he sustained in training and it will take at least another fortnight for him to return to action.
United are yet to take up the option to buy Falcao because of his latest injury, which comes 10 months after he damaged cruciate ligaments playing for Monaco.
"Do you think we expected he'd be injured for so many weeks? Because of that (injury setback) maybe we didn't buy him," the United manager said.
Falcao is one of the club's top earners, but his only meaningful contributions on the pitch so far have been an assist for Robin van Persie's goal against Leicester and his own strike in the victory over Everton.
Falcao admitted his spell on the sidelines had been "frustrating".
But his manager insists he has had no option but to keep the 28-year-old out of his squad.
"I don't give any chance to players when they are not fit, believe me," Van Gaal said.
"Look at my record and you will see that.
"You have to be fit
And what's your name? It doesn't matter - you have to be fit
I'm sorry
I have to manage with the other players and we believe in these players
And we shall show it."
When asked whether he expected to be justified in his decision to sell Danny Welbeck and loan Falcao, Van Gaal said: "I hope so
That is clear, I think."
Welbeck will be looking to prove a point when he faces the team he supported as a boy for the first time on Saturday.
Welbeck has scored five goals for Arsenal and the same amount for England since he last pulled on a United shirt.
Wayne Rooney and Robin van Persie have scored just three goals for United apiece.
Van Gaal stands by his decision to sell the United Academy product, who grew up in Longsight, just four miles away from Old Trafford.
He said: "We have Van Persie and (James) Wilson, and when you keep Welbeck, you don't give any chances to youngsters
That's also our philosophy, to give opportunities to youngsters.
"And then also we could buy Falcao
So (if) that is not enough reason, then I don't know - I'm not a very good manager," Van Gaal said.
"For him it was a very good decision because as a line-up player he develops himself much more.
"If it was right for Manchester United is dependable on how they play, how they score and in what position we shall finish in the league."
Van Gaal denied he gave up on Welbeck, insisting he was not the first United boss to omit the striker from the starting XI.
"Here, Danny Welbeck did not play every match
He was not a line-up player; he was more substitute than line-up," Van Gaal said.
"With different coaches not a line-up player, then came Mr van Gaal and the world is changing? No, the world is not changing - the facts are not my facts, they're the facts of Danny Welbeck."
A win at the Emirates would be a big boost for United, who lost at Manchester City and drew at home to Chelsea in their most high-profile games so far this term.
"It is remarkable," Van Gaal said when he was reminded he is still searching for his first away win with the club.
Earlier this week Van Gaal's boss Ed Woodward told club investors it would be unlikely the club would sign anyone in the January transfer window.
"We are not looking to enter the market for short-term fixes," said the executive vice-chairman, who was speaking on the day United posted a 9.9 per cent fall in revenue.
Van Gaal has no qualms with Woodward's words.
"I agree with that because if you buy, it has to be a player who is better than what you have in your squad
It shall be very difficult to find such a player," he said.
"We are speaking the same language."
Source : PA
Source: PA