But the final whistle came at the right time for Neath as Aberavon were still attacking and looked determined to get the converted try which could have swung the game their way.
"I'm pretty relieved," Horgan said. "We played well in the first half and looked like the better team. Our plan was coming to fruition and we were putting them under a bit of pressure.
"We lost it a bit in the second half especially after we went down to 13 man for a while but the boys dug in there. All in all I was pleased with their performance. We've got a cup final to prepare for now and who knows what will happen there."
Neath have suffered from injuries all season, a fact which makes their cup final appearance all the more rewarding. But Horgan's side return to league action and two games in a week, starting this Wednesday with a rearranged home game against Llanelli at The Gnoll (KO 7.15pm).
"We didn't know our side for the semi-final until less than hour before kick-off," Horgan admitted.
"Lee Evans pulled out just before the game. We were hoping he'd come through as he's a big player for us.
"Chris Morgans' yellow card could have been a big setback for us. But Gareth Gravell, Euros Evans and the other youngsters in our team all came through. It was the typical Neath spirit.
"We've dug in all season. I've nothing but praise for them really. We've a tough week now with Llanelli and Llandovery to come but our main focus now has to be this cup final and Pontypridd.
"There'll have to be changes on Wednesday as we've Llandovery three days after that. We've a few bumps from the Aberavon game so it worries me that such a strain has been put on a small squad.
"We had some fantastic support on Sunday and we look forward to seeing everyone back at The Gnoll this Wednesday."
Neath's opponents in the Millennium Stadium final will be Pontypridd who beat Carmarthen Quins 18-16 on Saturday.
"I'm sure Pontypridd will be favourites," Horgan added.
"But you can go back to the last cup final I played in for Neath when we took on Ponty. We were out and out favourites then and probably should have won on the day but Flanagan kicked a drop goal in the last minute to win.
"It's all about what happens on the day."