Any optimism about getting a good away result after Saturday’s opening day home win evaporated in a disappointing second half display on Tuesday.
A crowd of 109 saw Hillians more than hold their own in the first half and go in level at 1-1. Skipper Darren Budd, who is unavailable on Saturday, scored the equaliser.
But after the break the Sussex side then got a real ducking from the Swans, who were starting their home programme.
The Swans’ Will Turl did the most damage, netting a hat-trick, and the others on target were Greg Ngeno and Juan Onieva.
Afterwards Hillians manager Ian Chapman said: “It was shocking and about the worst night we could have had.
“We gave away goals from set-pieces and that was particularly worrying.
“I must take some of the blame because I took Neil Watts off at half time. He’d picked up a booking and I just wanted to protect him but in hindsight, it probably cost us .
“Also at 3-1 down we decided to chase the game and again that proved costly. Perhaps we should have regrouped.
“In the end they were too good for us but too many of our key players under performed and the way we lost our discipline was something I have not seen so badly since I came to the club.
“Rest assured, it will be something we’ll be addressing in training this week.”
The 34-year-old former Brighton player Paul Armstrong was rested but Chapman brought him on at half time, when Spencer Slaughter was switched to right back.
Hillians: Martin; Watts (Armstrong, 45), Pointing, Lake-Edwards, Fisk; Thompson, Budd, Slaughter, Kirkwood; Harding, Curd.
Stuart Tuck is still missing for this weekend and it is not known whether the returning Richard Greenfield will figure in the league trip to Tooting & Mitcham.