Sunday's 2-2 draw with Arsenal in the third round of the FA Cup means a replay will be needed to decide who faces Brighton in the fourth round, and adds another game to Swansea's already crowded January schedule.
Substitute Michu looked to have put the Swans on course for victory with his 58th-minute opener.
Goals from Lukas Podolski and Kieran Gibbs then put the Gunners 2-1 to the good with just six minutes remaining, only for Danny Graham to rifle home and force a replay.
As a result, Swansea face a two-legged Capital One Cup semi-final against Chelsea, Premier League fixtures against Everton, Stoke and Sunderland, the cup replay against Arsenal and a potential trip to meet Brighton before the month is out.
Laudrup had made it clear he would need to rotate his squad and that his fringe players would need to step up when called upon during this critical period.
And they have performed admirably thus far, with the draw against the Gunners extending Swansea's current unbeaten run to five games, despite leaving top scorer Michu on the bench and resting key defender Ashley Williams.
Laudrup said: "It shows we are building.
"To play against Arsenal and allow ourselves to have one of the league's top scorers on the bench and still stand up to Arsenal, one of the big teams in the Premier League, is great to see.
"It shows the depth of the squad is there and we will need it as this puts one more game on the table for us in January, when we already have a lot of games. It will be difficult but every footballer likes to play games."