Spanish midfielder Mata picked up to yellow cards in quick succession midway through the first half, reducing the Red Devils to ten men at The Hawthorns, as they went on to lose 1-0 courtesy of Salomon Rondon's second-half strike.
After the match van Gaal suggested that the negative result, which has the Red Devils three points out of the top four, was simply because of their opponents having extra personnel on the pitch.
"It's a big blow, these kinds of matches you have to win," said van Gaal on Sky Sports.
"We have played 60 minutes with 10 men against 11 and this is the fifth match in 14 days.
"It is very difficult to play against 11 and that's the reason we lost. We didn't give many chances away, only the goal really, it's a big pity that we had to play with 10."