Horgan said: "We were always aware of Bargoed's quality but showed plenty of enterprise to secure our place in the semi-final.
"There was a tremendous atmosphere and it was a good cup tie and a lot of praise for that is down to the referee who was excellent.
"We were disappointed to give away those two late scores but all the subs were on so we were a bit untidy and the game had already been won."
Paying their first visit to The Gnoll since 1923, Bargoed were on the back foot almost immediately as Neath made the perfect start. Splendid approach work by Kevin James paved the way for a wonderful try by Dai Langdon who arrowed across inside two minutes. The fly half converted his own score for a 7-0 lead.
Langdon quickly added a penalty as the home side maintained the momentum but they were forced into a back-line re-shuffle when scrum-half Luc Jones was injured.
Following a series of indiscretions by the visitors, Bargoed centre Simon Parry was yellow-carded and a team-mate might well have followed but referee Ian Davies felt they had been punished enough as Neath skipper Gareth Gravell touched down for the second home try. Langdon again converted.
Indiscipline was costing Bargoed dearly as Neath pieced together some thrilling rugby with centre John Leyshon a constant threat. The Welsh All Blacks more or less sewed up the tie on the half hour when flying winger Bowdy Davies crossed for their third try which Langdon again goaled.
At 24-0 down, Bargoed continued to battle and they got their reward just before half-time when former Ebbw Vale full back Andrew McLoughlin got his side back into it.
Bargoed outside-half Josh Prosser launched them into the second-half with a penalty but Neath played good, controlled rugby to keep possession into the wind with hooker Rhodri Clancy, flanker Lee Evans and fit-again lock Euros Evans, on as a replacement, at the heart of the effort.
Langdon's second penalty pushed Neath further ahead but Bargoed countered with a try by lock Lee Williams who benefited from a kind bounce. Prosser converted but Neath re-doubled their efforts and a good drive off a Jonny Griffiths line-out-take saw prop Roy Jones cross for his second try in successive home games.
By now Neath were very much in control and when Chris Morgans scored their fifth try, converted by Langdon to make it 39-15, that seemed to be it as the game had entered injury-time.
Neath utilised all eight replacements but, to their credit, Bargoed kept playing and two last-gasp tries by Parry and Craig Lynch, the first converted by Prosser made the final scoreboard look a lot better from their point of view.
Neath: Tries : Langdon, Gravell, Davies, Roy Jones, Morgans; Cons : D.Langdon (4); Pens Langdon (2)
Bargoed: Tries: McLoughlin, Williams, Parry, Lynch; Cons: Prosser (2); Pen: Prosser