Jack Wilshere scored a superb winner for Arsenal with four minutes left of normal time, and it was no more than the hosts deserved.
Swansea had set up the replay with a late Danny Graham goal in the 2-2 draw and Laudrup had no complaints to be denied by a similarly late goal at the Emirates.
Laudrup said: "The first half was very even, they had a bit more of the ball but we were at the same level.
"In the second half they were the better team, they deserved the win and good luck in the competition.
"They created chances and pushed us back, we defended great but we couldn't get out of there.
"It was nice to see Michel Vorm back at his best and we blocked a couple of big chances.
"They had one or two where you say 'How did they miss that?', and then they scored with a few minutes left.
"Last time it was us, this time it was them."