Both players were taken off at half-time of Sunday's FA Cup third round clash at Huish Park, to be replaced by Jonny Evans and Juan Mata.
The alterations meant United were forced to switch from a back five to a four, but the changes had little effect as a stunning strike from Ander Herrera and Angel di Maria's late goal earned them a 2-0 victory over their League One opponents.
Van Gaal revealed in his post-match press conference that Rafael had suffered a fractured cheekbone while Shaw had picked up an ankle problem.
Rafael had only recently recovered from a knock, while Shaw missed more than a month with a previous ankle injury.
After failing to create many chances of note in the first half, Van Gaal was pleased with the way his side came through a tricky tie in the second period, especially with the memories of a 4-0 thumping by third-tier MK Dons in the League Cup in August fresh in his mind.
"I had expected this. It is always difficult to play against a team like this - play long balls - you have to fight and they gave us a lot of pressure," the Dutchman told BBC Sport.
"We did not have time to play the ball around, we changed things a little bit in shape in the second half but that was necessary as Shaw was injured, as was Rafael.
"We then had more of the ball and that is why we could score the winner.
"We had more chances in the second half and our first goal came as a consequence of that. Then Yeovil attacked and we were able to score on the counter.
"It [the FA Cup] is important for every club, not just Manchester United. We want to win the FA Cup, we know it will be difficult but that is our goal."
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