The German star raised an arm to Winston Reid, but the officials failed to see the incident.
The German midfielder raised his arm to the New Zealand international in the first half, but the incident went unnoticed by the referee and he escaped punishment.
Had the referee seen the incident, or any of his assistants, it would have been a certain red for the Manchester United midfielder.
Bilic, though, refused to blame the ref, but insisted it was without doubt a red card.
"To be fair I didn't see it when it happened,” he told BBC Sport.
“At half-time they showed me and it's a clear red card. A straight red without any doubts.
"I said to the referee I can't blame him because he simply didn't see it and it happens. They were concentrating on the ball and I can't blame him no matter how disappointed we are."
The result, though, was a positive one for Bilic’s side, as they moved up to sixth in the table, just three points behind Tottenham Hotspur in fifth and six behind United in fourth.
In contrast, Van Gaal’s side slipped down the table, as they lost ground in this season’s title race as a result of the draw.
With Arsenal winning, they are now a point behind the Gunners who sit third, while Leicester City opened up a two-point lead at the top of the table by beating Swansea City.