United fell behind to an excellent volley from Cheikhou Kouyate following a first-half display of which Van Gaal was highly critical.
Radamel Falcao and Robin van Persie passed up clear opportunities as the visitors piled on late pressure, which was rewarded when Daley Blind struck in the second minute of injury time.
"I thought that we played a very bad first half," Van Gaal said. "West Ham were much better - they won every second ball.
"When we had the ball we lost the ball so easily without great pressure from West Ham. So it was very poor in the first half.
"In the second half after three minutes they scored and we gave that goal away.
"But then my team have shown fantastic spirit and also fantastic football.
"We created three open chances and also scored the goal.
"My opinion is that we could have won this game also, so I cannot say that I am very happy with the point because I am very disappointed about the poor first half.
"We can do much better, as you can see in the second half."
Van Gaal's decision to introduce Marouane Fellaini and adopt a more direct attacking approach during the closing stages was an important factor in his team earning a share of the spoils.
The Belgium international won praise from his manager, who also challenged other United midfielders to display similar battling qualities.
"I have done that already a lot of times with Fellaini so that is not new," he added. "I think also West Ham United should know that.
"With him we have more power - in Adnan [Januzaj] and [Angel] Di Maria we have more creative players.
"With these players you cannot always win the second ball, but you have to win. Otherwise I have to line up always with players like Fellaini."
