Dwight Tiendalli thanked the Jack Army for their support following Saturday's 5-0 home defeat against Chelsea.
The Swans were left with their heaviest home defeat since 1991 as the Barclays Premier League leaders ran riot at the Liberty.
Oscar opened the scoring inside the first minute, while the Brazilian international netted his second either side of a Diego Costa double in the first period.
It could have been worse for the hosts after Willian struck the crossbar shortly before the break, and Chelsea added a fifth late in the second half courtesy of substitute Andre Schurrle.
The result means Swansea remain ninth in the table, while Chelsea opened up a five-point gap on Manchester City.
And Tiendalli - making his first Premier League start of the season - praised the home fans for their support throughout what was a tough afternoon for Garry Monk's side.
"The supporters were great today," he said. "Even when it wasn't going well, they kept singing and getting behind us and we'd like to thank them for that.
"If you lose 5-0 it's always tough to take. We knew it was going to be a difficult game against a good side, but the defeat is unacceptable.
"We were unlucky to concede a goal so early and everyone was a bit down after that. We normally show such good spirit but it wasn't there today."