Gabriel Agbonlahor was dismissed in the 65th minute of Saturday’s contest after Radamel Falcao had equalised for United, but the visitors failed to create any clear opportunities in the final 25 minutes at Villa Park.
And Van Gaal, whose side could have picked up their seventh straight win in the Premier League, was left frustrated with just a point.
He told Sports: ???It???s disappointing not to win the game. We were the better team throughout the match.
???Villa scored against the run of play, we got back in it with a great goal, and we were pressing and pushing but our final cross wasn???t what we wanted.
???(After the red card) they defended a lot more and got more bodies behind the ball and made it difficult. We should have created more opportunities.???
United lost ground on Manchester City, who had earlier beaten Crystal Palace 3-0 at the Etihad Stadium, and are now seven points behind their rivals.
With Manchester United unconvincing in victory on occasions over the last month, Van Gaal was left regretting another below-par performance.
He added: ???I am very frustrated and I think the players also are because we were the better team and we don???t win. You have to win when you are the better team. In the first half we weren???t aggressive enough.
???I also have to say Aston Villa were well organised but when you allow them to score you know it will be very difficult.
???We pressed more in the second half and that???s why we scored but you have to score two times. We weren???t effective enough. It could have been seven in a row but it is not.???
Despite the draw, the Dutchman was delighted for Falcao, who scored only his second goal for the club since joining on loan from Monaco in the summer.
Van Gaal said: ???I???m very happy for him because he needed it. I???m always happy when a striker scores.???