Left-back Shaw is expected to miss at least six months after sustaining a double leg-break in United's Champions League loss at PSV on September 15.
United have tried four different players in the position, though none of Daley Blind, Marcos Rojo, Matteo Darmian or Ashley Young have yet convinced in the role.
And while United can return to the top of the Premier League standings with victory at Arsenal on Sunday, Van Gaal concedes that his team are still feeling the effects of the England international's absence.
Van Gaal said: "We lost Luke and that is a big blow. I said that this would be the year of Luke Shaw.
"His is the only position which we don't have a double option. So the circumstances are not so good for us.
"Four people have played in that position since Shaw’s injury. And we have won every game, but in my opinion, we don't have a good substitute for Luke Shaw with the same qualities.
"So it's a big blow."