The Swans have made an excellent start to the Barclays Premier League season, and lie second in the table after taking two wins and a draw from their first three games.
But the 2-2 draw with Sunderland at the Liberty Stadium 12 days ago came at a cost.
Left-back Neil Taylor suffered a broken ankle that will rule him out for the rest of the season, while centre-half Chico Flores was shown a straight red card and misses the next three games.
This week the club also lost Kyle Bartley for around three months with a ruptured quad.
Laudrup has brought in free agent Dwight Tiendalli to provide cover for young Ben Davies at left-back, while Alan Tate is set to partner Ashley Williams in central defence, although there will be no specialist replacement on the bench.
But Laudrup believes his side have the strength to manage.
He said: "It has been a bad couple of weeks. We all remember what happened to Neil and after that we have had another injury, not as serious, but a very difficult and rare muscle injury for Kyle.
"Then of course we have Chico suspended for three matches. It's typical, to lose three defenders like this.
"But we have a squad and we have prepared them to play from the beginning, we did not think about serious injuries at that time but we are covered, we have players.
"Dwight is coming in to cover left-back so we don't only have Ben for the rest of the season and I think we are covered."
While Swansea's defensive options have taken a hit, there is plenty of strength in midfield.
Ki Sung-yueng and Pablo Hernandez, the club's two most expensive signings, both look set for places among the substitutes at Villa Park thanks to the excellent performances of Jonathan de Guzman and Wayne Routledge.
In particular Laudrup is delighted by the competition for place between Routledge, Hernandez and Nathan Dyer.
He said: "We have three players for two positions, we have three great players and we all know Saturday is not the only game.
"We have a lot of games and to have three such good players is good for everyone. It is good for us as a club.
"Two will start and one will be on bench, and in some games we have the options to play all three.
"It brings competition and that means they will always keep themselves under pressure. If we had this in all positions it would be very good."
It was a difficult international period for some of the Swansea squad. Ashley Williams played in Wales' 6-1 hammering in Serbia, with Ben Davies and Jazz Richards on the bench, while striker Itay Shechter was part of Israel's 4-0 defeat to Russia.
But Laudrup expects his players to suffer no hangover.
He said: "We have players coming back from very different results, but now they are here and back in the group, hopefully they will recover so they are fit mentally for the game Saturday."