"It's about us really," said Horgan.
"If we can bring to the Swansea game what we've done well in certain parts of the last couple of games things will go okay.
"We just need to up that few per cent again in certain areas and take our opportunities. If we do that we'll win. If we don't it'll come down to a bounce of the ball and referee's decisions and at the moment they're not going our way."
Despite being in the bottom three alongside local rivals Aberavon and Friday's opponents, Horgan says that spirits are not down and that the players are improving week on week.
"The boys have worked hard again in training, just like they have for the last couple of weeks," he said.
"Our spirit is alright, there's no problem there. We just need to take our chances in every game we play at the moment.
"Nobody is beating us by playing exceptionally well. It's just us who are not taking our opportunities. As soon as we start doing that, the results will come.
"We're making strides every week to improve. Our line-out let us down last Saturday against Newport but our scrum was better than the week before. We're a small squad with a lot of injuries and each week is tough. We are plugging away and working hard."
Neath's injury list now includes Ospreys youngster Emyr Williams who is due to have a scan this week but Horgan was impressed with debutants Marc Jones and John Leyshon last weekend.
"Marc went well in the scrum and John worked hard in the centre," Horgan added.
"You couldn't ask for more in their first games. They'll be an essential part of the squad.
"It's a big game for us this week at Swansea and it'll be great to see a good crowd from Neath supporting us.
"As a team we need the support home and away and we'll keep working hard to get those results. If we keep committed, they will come."
Ian Hopkins, team manager at Swansea Rugby added:
"We are looking forward to playing Neath this evening and both sides are sure to be fired up due to the local rivalry.
"We were bitterly disappointed with the loss to Bridgend last week as I felt we had played well enough to get a win."
Swansea: 15 Rhys Williams 14 Christopher Shelmerdine 13 Nicholas Harwood 12 Benjamin Roberts 11 Liam Thomas Price 10 Cameron Clement 9 Jake Cole, 1 David Norman 2 Paul John 3 Ian Williams 4 Sam Kiley (c) 5 Rhodri Hughes 6 Robert Dudley-Jones 7 James Dax Bija 8 Daniel Baker.
Replacements: Andrew Littlehales, Nicky Smith, Aled Mason, Benjamin Fox, David Leonard, William Batcup, Aled Lewis, Lewis Harrhy.