The Foxes were again without forward Riyad Mahrez, who had missed training in the wake of a deadline-day move to Manchester City falling through.
Jamie Vardy gave Leicester the lead on 17 minutes and Swansea lost midfielder Leroy Fer to what looked a serious ankle injury after 34 minutes.
Foxes boss Claude Puel said: “It is a big frustration. I think first well done to Swansea because they defended very well. They had just one chance in the game and I think we played very well in the first half. We created a lot of chances. We created of chances with quality and good combinations, a good understanding.
“It was amazing but without the final the clinical edge. We had to score another goal in the first half because it was a good period with quality. We put them under pressure with all these chances.
“It was a bit more difficult in the second half and perhaps there was some tiredness. We finished the game stronger and it is a big frustration because we conceded one chance in the entire game and we conceded a set piece goal.
“It is harsh for the team but we have to correct this situation because we conceded a lot of goals from set pieces since the beginning of the season. We could have had a good reward after this game because of a lack of focus and concentration from a set piece. It is harsh."