The Hammers defeated the League One outfit thanks to two Craig Bellamy goals before half-time but Dyer had already been hospitalised by then.
The England man, who has suffered with a host of injury problems in recent years, now faces another lengthy spell on the sidelines just 12 days after completing his move from Newcastle to Upton Park.
Curbishley said: "We are so devastated for him. I can't put it into words really. The game was immaterial after that. You put a strong side out and you wonder why sometimes.
"We are delighted we have got through but after 10 or 15 minutes the game was immaterial. Everyone in the dressing room is really down about it."
Dyer had been hurt by a challenge from Rovers left winger Joe Jacobson and Curbishley intimated he and his players felt the challenge - which was punished by a free-kick only by referee Mike Jones, had been a reckless one.
He said: "I think the Bristol Rovers player has got to be very disappointed with his tackle. As far as I can see he has lashed out after losing the ball and caught Kieron in a difficult area.
"Wouldn't you be angry? The players could see he lashed out. But it is immaterial what the referee does after you get a serious injury like that."
Rovers manager Paul Trollope, who saw substitute Andy Williams pull a goal back to set up a tense finish, insisted the incident was not a deliberate attempt to cause injury.
He said: "It was a foul. He swung his leg back to try to win the ball and that was it. Our thoughts are with Kieron Dyer but Joe is not that type of player and we are not that type of football club. We don't tell our players to do that.
"Joe is an honest lad and he swung his leg to get the ball. It was just an unfortunate incident."