Rangers had Martin Rowlands sent-off just eight minutes into the second half and the home side took advantage when Mark Gower opened the scoring on 74 minutes.
Rangers were reduced to nine men on 77 minutes when Ben Watson was dismissed and the Swans doubled their advantage five minutes from time.
"We started really well but should have scored in the first half," Magilton said after the 2-0 defeat.
"Swansea came out much better after the interval but their keeper still had to make a couple of great saves to stop us from taking the lead.
"It was two influential players who were dismissed and today we carried one or two others but we still tried to play positive football despite the setbacks.
"I felt comfortable for the opening half hour but that lack of a cutting edge has cost us."