United have yet to win a competitive game under the former Netherlands coach and could have few complaints about Saturday's result at Turf Moor.
Although Van Gaal's men were unfortunate not to be awarded a late penalty when a shot from Ashley Young appeared to be handled by Burnley substitute Ashley Barnes, the hosts were good value for a share of the spoils having created a number of opportunities of their own.
Ex-United midfielder David Jones struck the crossbar early on, while Burnley goalkeeper Tom Heaton was rarely tested despite occasional flashes of class from visiting debutant Angel di Maria.
Reflecting on a third-successive Premier League game without victory, Van Gaal told BT Sport: "I don't think we give a lot away, but we have to create more chances and today I think we have created chances to score.
"I think we were the stronger team, certainly in the second half.
"Of course the progress is there, but you have to win. A club as [big as] Manchester United have to win.
"When you have two points [out] of [a possible] nine... that is disappointing."
"I think a manager don't have to discuss these issues [the penalty claims]," added the Dutchman.
"You have to see the match and I think we have a lot of free-kicks against us, and I'm certain we have more ball possession, so how is that possible?"
"I believe when we play against Queens Park Rangers [after the international break], Rojo shall have a permit," Van Gaal stated.
