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."
Among those to shine at the Liberty Stadium was summer signing Kyle Bartley, who excelled in the heart of defence on just his second appearance since joining from the Gunners for £1million.
Laudrup said: "He has been very unlucky. He would have had a run in the side when Chico had a red card against Sunderland, and the next day he suffered an injury that kept him out for three months.
"When he came back Garry Monk had just had two or three games where he did well, and Chico and Ashley have been doing great this season.
"It's difficult as we have four very good centre-backs, but we can only play two and have one on the bench.
"But I want to see what Kyle can give us for the present and for the future, and I felt with this game against his old team it was a good game for him, and he proved me right."
Arsenal manager Arsene Wenger also took the opportunity to praise full-back Gibbs for his performance.
Aside from his goal, the 23-year-old was typically industrious up and down the left-flank, adding an extra dimension to Arsenal's attacking threat while being solid in his defensive duties.
Wenger said: "I thought Kieran Gibbs had an outstanding game, he gets better and better and in these type of games it is very positive to see."