The 23-year-old Wales international, who featured for Team GB at the Olympics, dislocated and broke his ankle in three places after his lower left leg buckled under him as he challenged Craig Gardner.
Ben Davies replaced Taylor on Saturday and the 19-year-old could now be set for a run in the team. However, Taylor's injury is a big concern for Laudrup and the Dane wants to bolster his defence.
"Neil's injury is serious first of all for him as a person and a player," he told the South Wales Evening Post. "One second you are out on the pitch running and playing, then suddenly you are out.
"You are talking a long time before Neil returns to the game, and we will have do something. We only have one left-back now and he is only 19, so we will see what we can do.
"Ben did well in pre-season and he did great against Sunderland, but he is 19 - you can't put so much responsibility on his shoulders. We can't go out and buy someone, but we need someone. We will have to wait and see what possibilities we have. What happens if Ben gets an injury or a little flu or whatever? We need an extra player."