The Dane was without Michu at Stamford Bridge after the star forward was ruled out for six weeks due to ankle surgery while goalkeeper Michel Vorm and midfielder Nathan Dyer are also long-term absentees.
To make matters worse for Laudrup, whose side have now won just twice in 14 games in all competitions, record signing striker Wilfried Bony is only just working his way back to full fitness and could only come on as a second-half substitute at Chelsea.
And Laudrup told Sky Sports after the final whistle: "I think we are a little short now, because we are talking about the injuries. It is not just two weeks, we are talking several weeks.
"A part of that is just very small injuries. If you have two or three injuries, you can always cope. As long as you have 18 or 19 players, it is enough.
"But at the moment we have a couple of important injuries for a longer time and that is why maybe we have to do something in January.
"But one thing is to want to do something and another thing is to find the right ones, because a lot of teams are looking, especially for players who can score goals, in the transfer window."
Eden Hazard's first-half goal gave Chelsea the points on Boxing Day as Swansea managed only one shot on target in the entire game at Stamford Bridge.
But Laudrup was still encouraged by the performance of his team ahead of a crucial game at fellow strugglers Aston Villa which comes as soon as Saturday.
"It was important for me to see that we stayed in the game against a team like this [Chelsea] until the last second, believing we could get something," said Laudrup.
"Again, we did not [get something] but we have to bring these positive things along to the next game."