The Dutchman saw his side labour at Villa Park, with United unable to break Villa down even when Gabriel Agbonlahor was sent off after the hour mark.
Radamel Falcao cancelled out Christian Benteke's opener, but Van Gaal's men failed to make it six Premier League wins on the spin.
Van Gaal was left to bemoan his team's inability to get a second goal and maintain their great run of form.
"We dropped two points, we were the better team I think and that's frustrating when you are the better team and don't win these kind of games," he said.
"When you want to be part of the title race, you have to win these games and I think also that we were not so aggressive in the first half than we are normally.
"We kept the ball much better but we didn't create so much because we were not looking to the forwards.
"It was not good enough to get the victory here and were not creative enough in the second half and didn't keep the ball as well in the first half.
"We had more aggression so that was the plus I think. We have the draw and that's why I'm a little bit frustrated, we could have won this game in my opinion and we didn't do that."
Van Gaal did reserve special praise for Falcao, who scored his first United goal since October after struggling for game time due to recent injury problems.
"It was a beautiful goal and I am very happy for him," he said, before admitting that the Colombian is not guaranteed to start against Newcastle United on Boxing Day.
"I have to compare every week, not only for Falcao but for every player," Van Gaal added.
